{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Threshold_Free_Metrics)=\n",
    "# Threshold-free metrics\n",
    "\n",
    "All the metrics presented in the previous section can only be computed once a confusion matrix is available, which requires setting a decision threshold $t$ on the probabilities that are returned by the classifier. In order to evaluate the performance of a classifier over a range of different thresholds, two well-known assessment techniques are the Receiving Operating Characteristic (ROC) curve and the Precision-Recall (PR) curve. Both techniques allow providing an overall performance score, in the form of the area under the curve (AUC) measure.\n",
    "\n",
    "This section presents these two techniques and discusses their pros and cons. In particular, we will show that the PR curve and the Average Precision (as the metric that computes the area under the PR curve) are better suited for fraud detection problems than the ROC curve and the AUC ROC, respectively.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n",
      "                                 Dload  Upload   Total   Spent    Left  Speed\n",
      "100 37136  100 37136    0     0   148k      0 --:--:-- --:--:-- --:--:--  148k\n"
     ]
    }
   ],
   "source": [
    "# Initialization: Load shared functions and simulated data \n",
    "\n",
    "# Load shared functions\n",
    "!curl -O https://raw.githubusercontent.com/Fraud-Detection-Handbook/fraud-detection-handbook/main/Chapter_References/shared_functions.py\n",
    "%run shared_functions.py\n",
    "\n",
    "# Get simulated data from Github repository\n",
    "if not os.path.exists(\"simulated-data-transformed\"):\n",
    "    !git clone https://github.com/Fraud-Detection-Handbook/simulated-data-transformed\n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Receiving_Operating_Characteristic_Curve)=\n",
    "## Receiving Operating Characteristic (ROC) curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Receiving Operating Characteristic (ROC) curve {cite}`fawcett2004roc,fawcett2006introduction` is obtained by plotting the Recall (or True Positive Rate - TPR) against the False Positive Rate (FPR) for all the different classification thresholds $t$. It is the *de-facto* standard for estimating the performance of fraud detection systems in the literature {cite}`dal2015adaptive`. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A classifier K is said to be more performant than a classifier W in the ROC space only if the curve of K always dominates the curve of W. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    \n",
    "![](images/ROC.jpg)\n",
    "</center>\n",
    "\n",
    "<div align=\"center\">Fig. 3. The Receiving Operating Characteristic (ROC) curve for two classifiers K and W. <br>The gray line represents the performance of a random model.</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The best classifier corresponds to the point (0,1) in the ROC space (no false negatives and no false positives), while a classifier predicting at random would have performances along the diagonal connecting the bottom left corner to the\n",
    "top right. When there is not a clear winner (e.g. classifier K dominates W only in one part of the ROC space), the comparison is usually done by calculating the Area Under the ROC Curve (AUC ROC). The AUC ROC is usually computed with the *trapezoidal rule* (linearly interpolation) {cite}`fawcett2006introduction`, which provides an expected probability for the TPR and FPR in case of ties in the prediction values.\n",
    "\n",
    "The ROC curve is obtained by computing the TPR and FPR for all possible fraud probability values returned by a classifier.\n",
    "\n",
    "Let us illustrate its construction by reusing the simple example presented in the [previous section](Threshold_Based_Metrics). The example contains 10 transactions, among which 2 are fraudulent, and 8 genuine. The labels are given by a list `true_labels`. We assume that a vector of fraud probabilities has been returned by a fraud detector.  The vector of fraud probabilities is given by a list `fraud_probabilities`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2 fraudulent and 8 genuine transactions\n",
    "true_labels = [1,1,0,0,0,0,0,0,0,0]\n",
    "\n",
    "# Probability of fraud for each transaction\n",
    "fraud_probabilities = [0.9,0.35,0.45,0.4,0.2,0.2,0.2,0.1,0.1,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first steps in computing the ROC curve consists in getting the list of all unique possible thresholds for which the TPR and FPR will be computed, and sort them by decreasing order. A threshold higher than 1 (set to 1.1) is also added for having the case where all transactions are predicted as genuine. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.1, 0.9, 0.45, 0.4, 0.35, 0.2, 0.1, 0]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unique_thresholds = [1.1]+list(set(fraud_probabilities))\n",
    "unique_thresholds.sort(reverse=True)\n",
    "unique_thresholds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives a list of eight unique thresholds to consider in this example. To these thresholds are associated all the possible (TPR, FPR) that the classifier can return.\n",
    "\n",
    "Reusing the `threshold_based_metrics` function defined in the previous section, let us compute the TPR and FPR for each of these thresholds. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Threshold</th>\n",
       "      <th>TPR</th>\n",
       "      <th>FPR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.90</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.45</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.40</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.35</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.20</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.10</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.00</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Threshold  TPR    FPR\n",
       "0       1.10  0.0  0.000\n",
       "1       0.90  0.5  0.000\n",
       "2       0.45  0.5  0.125\n",
       "3       0.40  0.5  0.250\n",
       "4       0.35  1.0  0.250\n",
       "5       0.20  1.0  0.625\n",
       "6       0.10  1.0  0.875\n",
       "7       0.00  1.0  1.000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "performance_metrics=threshold_based_metrics(fraud_probabilities, true_labels, unique_thresholds)\n",
    "performance_metrics[['Threshold','TPR','FPR']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the lower the threshold, the higher the TPR (more frauds are detected), but the higher the FPR (more genuine transactions are classified as fraudulent). The first point of the curve consists in predicting all transactions as genuine (threshold 1.1). The resulting TPR is zero (no detected fraud), and FPR is 0 (no false positive). The last point of the curve consists in predicting all transactions as fraudulent (threshold 0). The resulting TPR is one (all frauds detected), and FPR is 1 (all genuine transactions misclassified as frauds). \n",
    "\n",
    "Since the ROC curve is a standard metric in classification, the Python library `sklearn.metrics` provides a function `roc_curve` to compute the thresholds, as well as the corresponding FPR and TPR. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.   , 0.   , 0.125, 0.25 , 0.25 , 0.625, 0.875, 1.   ]),\n",
       " array([0. , 0.5, 0.5, 0.5, 1. , 1. , 1. , 1. ]),\n",
       " array([1.9 , 0.9 , 0.45, 0.4 , 0.35, 0.2 , 0.1 , 0.  ]))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FPR_list, TPR_list, threshold = sklearn.metrics.roc_curve(true_labels, fraud_probabilities, drop_intermediate=False)\n",
    "FPR_list, TPR_list, threshold"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now plot the resulting ROC curve. We note that the first threshold (1.9) differs from the one we chose earlier (1.1). This is because the `sklearn.metrics.roc_curve` function sets the first threshold to 1 plus the second threshold (0.9), giving 1.9 in this case. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "def get_template_roc_curve(ax, title,fs,random=True):\n",
    "    \n",
    "    ax.set_title(title, fontsize=fs)\n",
    "    ax.set_xlim([-0.01, 1.01])\n",
    "    ax.set_ylim([-0.01, 1.01])\n",
    "    \n",
    "    ax.set_xlabel('False Positive Rate', fontsize=fs)\n",
    "    ax.set_ylabel('True Positive Rate', fontsize=fs)\n",
    "    \n",
    "    if random:\n",
    "        ax.plot([0, 1], [0, 1],'r--',label=\"AUC ROC Random = 0.5\")\n",
    "\n",
    "ROC_AUC = metrics.auc(FPR_list, TPR_list)    \n",
    "    \n",
    "roc_curve, ax = plt.subplots(figsize=(5,5))\n",
    "get_template_roc_curve(ax, \"Receiver Operating Characteristic (ROC) Curve\",fs=15)\n",
    "ax.plot(FPR_list, TPR_list, 'b', color='blue', label = 'AUC ROC Classifier = {0:0.3f}'.format(ROC_AUC))\n",
    "ax.legend(loc = 'lower right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roc_curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ROC curves have three important properties {cite}`fernandez2018learning`. First, they are monotonic functions: The TPR can only increase as the FPR increases. Second, the area under the curve has a probabilistic interpretation: The AUC ROC can be interpreted as the probability that the scores given by a classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one. Third, the AUC ROC of a random classifier is $0.5$.   \n",
    "\n",
    "The last property can be easily checked by setting all predictions to 0.5. This gives a list of only two thresholds. The first is 1.5, which classifies all predictions as genuine. The second is 0.5, which classifies all predictions as fraudulent.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0., 1.]), array([0., 1.]), array([1.5, 0.5]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 fraudulent and 8 genuine transactions\n",
    "true_labels = [1,1,0,0,0,0,0,0,0,0]\n",
    "\n",
    "# Probability of fraud for each transaction\n",
    "fraud_probabilities = [0.5]*10\n",
    "\n",
    "FPR_list, TPR_list, threshold = metrics.roc_curve(true_labels, fraud_probabilities, drop_intermediate=False)\n",
    "FPR_list, TPR_list, threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "\n",
    "ROC_AUC = metrics.auc(FPR_list, TPR_list)    \n",
    "    \n",
    "roc_curve, ax = plt.subplots(figsize=(5,5))\n",
    "get_template_roc_curve(ax, \"Receiver Operating Characteristic (ROC) Curve\\n Random classifier\",fs=15,random=False)\n",
    "ax.plot(FPR_list, TPR_list, 'b', color='blue', label = 'AUC ROC Classifier = {0:0.3f}'.format(ROC_AUC))\n",
    "ax.legend(loc = 'lower right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roc_curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This results in a line going from [0,0] to [1,1]. The resulting AUC ROC is the area under this line, which is 0.5.\n",
    "\n",
    "Let us now reuse the experimental setting of the [baseline fraud detection system](Baseline_FDS) presented in Chapter 3. One week of data is used for training, and one week for testing. Five prediction models are considered: logistic regression, a decision tree with depth two and a decision tree of unlimited depth, a random forest with 25 trees, and a boosting model with default parameters. The ROC curves and their AUC are reported below for the five models.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Load  files\n",
      "CPU times: user 196 ms, sys: 155 ms, total: 351 ms\n",
      "Wall time: 375 ms\n",
      "201295 transactions loaded, containing 1792 fraudulent transactions\n",
      "Time to fit the Logistic regression model: 0.73\n",
      "Time to fit the Decision tree with depth of two model: 0.45\n",
      "Time to fit the Decision tree - unlimited depth model: 1.3\n",
      "Time to fit the Random forest model: 9.15\n",
      "[10:53:15] WARNING: /private/var/folders/wz/86tkhhmd5gxgh4f24bdl9l2m0000gn/T/pip-install-o8iul8v_/xgboost/build/temp.macosx-10.9-x86_64-3.8/xgboost/src/learner.cc:1061: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.\n",
      "Time to fit the XGBoost model: 7.49\n"
     ]
    }
   ],
   "source": [
    "# Load data from the 2018-07-25 to the 2018-08-14\n",
    "\n",
    "DIR_INPUT='./simulated-data-transformed/data' \n",
    "\n",
    "BEGIN_DATE = \"2018-07-25\"\n",
    "END_DATE = \"2018-08-14\"\n",
    "\n",
    "print(\"Load  files\")\n",
    "%time transactions_df=read_from_files(DIR_INPUT, BEGIN_DATE, END_DATE)\n",
    "print(\"{0} transactions loaded, containing {1} fraudulent transactions\".format(len(transactions_df),transactions_df.TX_FRAUD.sum()))\n",
    "\n",
    "\n",
    "start_date_training = datetime.datetime.strptime(\"2018-07-25\", \"%Y-%m-%d\")\n",
    "delta_train=delta_delay=delta_test=7\n",
    "\n",
    "(train_df,test_df)=get_train_test_set(transactions_df,start_date_training,\n",
    "                                      delta_train=delta_train,delta_delay=delta_delay,delta_test=delta_test)\n",
    "\n",
    "output_feature=\"TX_FRAUD\"\n",
    "\n",
    "input_features=['TX_AMOUNT','TX_DURING_WEEKEND', 'TX_DURING_NIGHT', 'CUSTOMER_ID_NB_TX_1DAY_WINDOW',\n",
    "       'CUSTOMER_ID_AVG_AMOUNT_1DAY_WINDOW', 'CUSTOMER_ID_NB_TX_7DAY_WINDOW',\n",
    "       'CUSTOMER_ID_AVG_AMOUNT_7DAY_WINDOW', 'CUSTOMER_ID_NB_TX_30DAY_WINDOW',\n",
    "       'CUSTOMER_ID_AVG_AMOUNT_30DAY_WINDOW', 'TERMINAL_ID_NB_TX_1DAY_WINDOW',\n",
    "       'TERMINAL_ID_RISK_1DAY_WINDOW', 'TERMINAL_ID_NB_TX_7DAY_WINDOW',\n",
    "       'TERMINAL_ID_RISK_7DAY_WINDOW', 'TERMINAL_ID_NB_TX_30DAY_WINDOW',\n",
    "       'TERMINAL_ID_RISK_30DAY_WINDOW']\n",
    "\n",
    "classifiers_dictionary={'Logistic regression':sklearn.linear_model.LogisticRegression(random_state=0), \n",
    "                        'Decision tree with depth of two':sklearn.tree.DecisionTreeClassifier(max_depth=2,random_state=0), \n",
    "                        'Decision tree - unlimited depth':sklearn.tree.DecisionTreeClassifier(random_state=0), \n",
    "                        'Random forest':sklearn.ensemble.RandomForestClassifier(random_state=0,n_jobs=-1),\n",
    "                        'XGBoost':xgboost.XGBClassifier(random_state=0,n_jobs=-1),\n",
    "                       }\n",
    "\n",
    "fitted_models_and_predictions_dictionary={}\n",
    "\n",
    "for classifier_name in classifiers_dictionary:\n",
    "    \n",
    "    start_time=time.time()\n",
    "    model_and_predictions = fit_model_and_get_predictions(classifiers_dictionary[classifier_name], train_df, test_df, \n",
    "                                                          input_features=input_features,\n",
    "                                                          output_feature=output_feature)\n",
    "    \n",
    "    print(\"Time to fit the \"+classifier_name+\" model: \"+str(round(time.time()-start_time,2)))\n",
    "    \n",
    "    fitted_models_and_predictions_dictionary[classifier_name]=model_and_predictions\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "roc_curve, ax = plt.subplots(1, 1, figsize=(5,5))\n",
    "\n",
    "cmap = plt.get_cmap('jet')\n",
    "colors={'Logistic regression':cmap(0), 'Decision tree with depth of two':cmap(200), \n",
    "        'Decision tree - unlimited depth':cmap(250),\n",
    "        'Random forest':cmap(70), 'XGBoost':cmap(40)}\n",
    "\n",
    "get_template_roc_curve(ax,title='Receiver Operating Characteristic Curve\\nTest data',fs=15)\n",
    "    \n",
    "for classifier_name in classifiers_dictionary:\n",
    "    \n",
    "    model_and_predictions=fitted_models_and_predictions_dictionary[classifier_name]\n",
    "\n",
    "    FPR_list, TPR_list, threshold = metrics.roc_curve(test_df[output_feature], model_and_predictions['predictions_test'])\n",
    "    ROC_AUC = metrics.auc(FPR_list, TPR_list)\n",
    "\n",
    "    ax.plot(FPR_list, TPR_list, 'b', color=colors[classifier_name], label = 'AUC ROC {0}= {1:0.3f}'.format(classifier_name,ROC_AUC))\n",
    "    ax.legend(loc = 'upper left',bbox_to_anchor=(1.05, 1))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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27RotW7bE3d2dpKQkpkyZwt27dwkNDWXixImEh4djZ2dXYDmaNGmCoaEh69ev1/blAXBycqJ27dqMHz+e3377jbCwMKZNm8avv/5KlSpV3vo6TU1NWbhwIfv379dey/Pnzzl16hRubm6kpKRo52XKtX//fnbs2EFYWBiLFi0iNDRUOwfaqFGjOHjwIGvXriU8PJyTJ08yY8YM9PT0Cu0MbWFhQWRkJGfPniUyMpL9+/drA7Xcjt+GhoY8ffpUG7C8i8aNG1OzZk28vLy4ceMG169f104RUViwYGVlxfTp09m0aRMzZszgxo0bhIeHExgYyNdff03btm21NaFvYmFhwd27d/n999958uQJW7Zs0U7Pkbdje17m5uakpKRw+PBhIiMjOX78uLaGLPecot41Q0NDAO7evUt8fPxbvbtvEhkZycyZM7lw4QKRkZEEBQWRnJyMo6MjUPQzcnNzIyYmhtmzZ/Pw4UPOnj3LsmXLChy1CDmjMvv06cO4cePYsGEDDx8+5O7duyxatIilS5cyadIkbeBVu3ZtDh48yNWrV7l//z5TpkwpsAbyzz70Z0sQBOF9+SSbGgtib2/PyJEjWbZsGcePH6dt27Zs2rSJuXPnMmjQICQSCbVr18bX11c7tN3Dw4P09HTmz59PXFwclStXZvXq1dovt02bNrFgwQL69euHnp4ejRo1YsmSJYUGJVKplG7durF58+Z8/c0kEgkrVqxg3rx5jB49moyMDBwcHLQ1a+/CycmJ3bt3s3btWr755hvi4+MpXbo0HTp0YPjw4a81tfXs2ZPg4GC8vb2pXLky69at09Z4tWjRAh8fH9auXcvSpUuxsLCgR48eTJgwodD8c6d+mDBhAllZWdjb2zNz5kymTp1KaGgo9vb2uLm5MWnSJLp06cKxY8fe6fogZ3TfzJkzcXNzw9jYGE9PT27cuFFkk13Pnj0pVaoUGzduxNPTE6VSSfny5fH09MTd3f2tvtwBvvnmG6Kjoxk2bBg6OjpUrVqVuXPnMmHCBEJDQ1/rdwU5fZBCQ0Px9vYmNTWV8uXLM3r0aNauXUtoaCgtWrR447s2cOBAFixYwIULF1ixYsUb3903mTZtGvPmzePbb78lISEBW1tb5syZo23uK+oZWVtbs27dOhYsWECPHj2wsLCgT58+BY7ozeXt7Y2joyOBgYGsWrUKyKmNWrJkSb4RuhMnTmTGjBkMHjwYY2Njhg4dmq8GrDDF8dkSBEF4Hz65meuFt9emTRv69OmTb4TiP11cXBzXr1+nefPm2mDp5cuXNGvWjICAgAIDH0EQBEH4p/hsaryET4OOjg7jxo1j8ODB9OnTB6VSyZIlS7C1tdU2kwmCIAjCP9Vn0cdL+HSYmpqyevVqQkJCcHZ2ZuDAgchkMjZu3PjOowMFQRAEobiJpkZBEARBEIRiImq8BEEQBEEQiokIvIRiM2XKFKpWrVroT5s2bf5W+mlpaQQEBLzTOStXrnynfBMSEti1a9e7Fk0QBEEQANG5XihG33//Pd9++y0Az58/p2/fvqxcuVK7VM7bTulQmM2bN7Nz507tDPQfwoIFC3j8+LF2/UpBEARBeBci8BKKjbGxsXZJG5VKBeR0li9ssex3VRzdFUWXSEEQBOHvEE2Nwj/KsWPH6NatGzVr1qRTp05s2LAh39I0a9eupW3bttSoUYOOHTtqmxb37NnDkiVLiIyMpGrVqly4cKHA9A8dOkTnzp2pVasWw4cP1y7dk+vOnTuMGDGC+vXra/PYt28fkDNx665du7h48SJVq1bl6dOnqFQq5syZQ+vWralRowaNGzdm6tSppKWlfaA7JAiCIPybiRov4R/j1KlTTJo0iWnTptGwYUPu37/PrFmzSEtLY8yYMZw4cYINGzawePFiypcvz7lz55g+fTpVqlShS5cuPHr0iODgYHbt2lXgYtiXLl1i4sSJTJw4kfbt23Pq1Cl8fHwoVaoUAKmpqQwdOpTWrVsTGBiIRqNh06ZNTJs2jWbNmjF06FDCw8OJjIxk2bJlWFhY8OOPP3LmzBnmz59PqVKluH79urYv2+DBg4v5DgqCIAj/dCLwEv4xVq9ejYuLi7b/VPny5VEqlUyfPp3Ro0cTERGBXC6nTJkylC1blr59+2JjY0PFihXR09PDwMAAHR2dQpsuAwICaNSoEZ6engBUqFCBq1evahenTktLY/DgwQwcOBB9fX0ARo4cyc6dOwkPD6d+/fro6ekhl8u1eTg6OtK1a1fq1asHgI2NDVu3bn3rxaoFQRCEz4sIvIR/jNu3bxMaGsr27du127Kzs0lPTycyMhJnZ2d27dpFhw4dqFKlCs2aNaNbt25vvT7h/fv3X1vIuXbt2trAy9LSEldXV/bt28ft27cJDw/nzp07AGRlZRWYZvfu3Tlz5gw+Pj6Eh4fz4MEDIiIisLGx+Su3QBAEQfjEicBL+MeQy+UMHz4cZ2fn1/ZZW1ujUCgICgri8uXLnDlzhlOnTuHr68u8efMKPOfPJBLJa53j8852Hx0dTf/+/bG2tqZ169a0atWKkiVL0rt370LTnDZtGseOHaNnz5506NCBCRMmMGvWrHe4akEQBOFzIgIv4R+jUqVKhIeHY2trq9129OhRDh48iI+PD4cOHSI+Ph43NzcaNGjAhAkTGDFiBEFBQTg7OyORSIpMv1q1aly9ejXfths3buTLS6lUEhAQoJ3a4n//+x/wx2jGvHmkpKSwe/dulixZQocOHQBQq9U8efKEMmXK/I07IQiCIHyqxKhG4R9j1KhRHDx4kLVr1xIeHs7JkyeZMWMGenp6KBQKMjIymDdvHkFBQURGRnL+/Hlu3bqlXRzb0NCQxMREHj16pJ2uIq9BgwYRGhrKokWLCAsLY/v27Rw6dEi739zcnJSUFA4fPkxkZCTHjx/nhx9+ACAjI0ObR1RUFE+ePEFXVxcDAwOOHz9OREQEt27d4ttvv+X58+fa4wVBEAQhL7FWo/BRPH36lLZt2xIQEED9+vW124ODg1m7di1hYWFYWFjQtWtXJkyYgEKhAGDDhg1s376d58+fY2lpSbdu3Rg3bhwymYyoqChGjBjBo0ePWLhwIR07dnwt39OnT7Nw4UIePXpEjRo1aNiwIcHBwZw4cQKNRoOPjw/79+8nNTWV8uXL4+Hhwdq1a+nevTtff/01d+/eZfTo0URHRxMQEEBiYiLz5s0jIiICCwsLWrRogaGhIceOHePo0aPFdj8FQRCEfwcReAmCIAiCIBQT0dQoCIIgCIJQTETgJQiCIAiCUExE4CUIgiAIglBMROAlCIIgCIJQTETgJQiCIAiCUEyKdQLVa9eusWDBArZs2ZJv+4kTJ1ixYgUymYzevXvTr1+/N6aVlZWlXcZFR0en0CVd/u0+1Wv7VK8LxLX9G+W9rtypSwRBED6EYgu81q1bR1BQkHbx4VyZmZnMmTOHXbt2oa+vj4uLC61bty50oeNcWVlZxMbGAjlr7OX++1PzqV7bp3pdIK7t38jE1JykxHgASpcu/ZFLIwjCp6zYAq/y5cuzbNkyvLy88m1/+PAh5cuXx9TUFIB69erx22+/0blz5+IqmiAInxj//frsPapf6P7IqHRepmQhlUOGQp8sRymX3MIpXdGu+AopCMJnqdgCr44dO/L06dPXtqekpGBsbKz93dDQkJSUlDemp6Ojg6WlJQAymUz770/Np3ptn+p1gbi2j239DilePjn/tZnqPgcgW6qDWqFALVeQpZCTrWMKpiDNysQgPQGnp+epXrcDUh3R7VUQhA/roy+SbWRkhFKp1P6uVCrzBWKFEU2N/26f6nWBuLbillu7FRWVSszLNJIyXy1QbngZ3Q4GJJUqTbqpGQD6aQk43DtKlbu/0jTlDF1KqTFavAurMp201yWaGgVB+JA+euBlb2/P48ePSUhIwMDAgN9++41hw4Z97GIJgvAP9edmxPNXdXP+IUsEfSOkVplkO8qhdj3SdLKok3QHu1/mY/vbz1SOu0Y1pxJUtq1OiU2XSe3bj0R54U2Sf1dmZiYRERGkp6d/sDwEQfhn0dPTo3z58sjl8gL3f7TAKzg4mNTUVPr378+UKVMYNmwYGo2G3r17Y21t/bGKJQjCP9zeo/rcuCentG0WL5KykJbODbRKotCoaVZSTe30e5T7eQ2KHauRZGRSphxU7lgDqyHbMPA7jtGatSjd3UmaOxekH655MSIiAh0dHUqWLIlEIvlg+QiC8M+g0WhQKpVERERgb29f4DHFGnjZ2NgQGBgIgLOzs3Z7mzZtaNOmTXEWRRCEj+RNHd/zym0+zJZKyVIoUCsUZCbLwVpKcjcppGvg4WPKp8fSLTaTvtJzPP3vGhLvPUKhC1VqSqjYqyMK58moraph8MMPGK1bh3LIEJK8veEDB0Pp6eki6BKEz4hEIsHQ0JDo6OhCj/noTY2CIHx6igqucpsGneqoCj1fnS0hIiaDqCQpmFuCrgKQgEaDjiwDE6NnlD14HcOYaPo2lvKF6n888Q7kZmoaViWhRRcFZfq7k9F4NNnGZVC/Sjezbl1SRo0iedq0Dx505RJBlyB8Xt70mReBlyAI70XeYKuo4Mqpjoqe7dNw756m3ZacKeFCnIKzMQoO3MsmUmoEUgVkqrGXJNPriwyaWKqobZaJrg5kqSQ8PxRJmJ8vsf+9SIRMgn1VDQ5OZhh++RVpjoNI182ZooasLOQ3bpDp6Eh69+6kd+/+4W/GP5C/vz+BgYHs3LkTXV1dvL29adeuHY0bN9Ye4+zsTHBwMACnT5/WtlCoVCpcXV1p3bp1vjS9vb25d+8eJiYmaDQaEhMTcXFxoWvXrgBcvnyZzZs3o9FoyMzMpHXr1vTv3x+JREJ2djZbtmwhJCQEHR0dACZMmPBa80xu9xOpVEpWVhZpaWlMnjwZBweHv3wvQkJCOHbsGNOmTfvLabyLhIQE/vOf/6BSqbCysuL7779HT08v3zFeXl4kJSUhk8nQ1dVl4cKFxVI2ofiJwEsQhPdi71F9bt6X80XlzAKDq7xS1BJ+jdZl3elkLiXpo7S0AqkUSVYWmodP4N4VqsuScWtizBD3qtrzlE+e8NDfn/CtAWTExmFiIcOpFVRqVh51izGkVetNqizPF5pajdm4cegdOMDLEyfIKqTPxefgyJEjtG3blmPHjmkDo8KEhoayY8cO5s+fj4GBAYmJiXh6emJnZ0eFChXyHTt69Ght8JaUlIS7uztdunQhLCyM5cuXM3/+fKysrFCr1SxYsICtW7fi5uZGQEAAiYmJrFixAqlUyu3bt5kyZQrbtm1DJsv/1bRo0SJ0dXOC+QsXLrBx40bmz5//Hu/Oh7Vp0ybat29P165d2bJlC/v27WPAgAH5jomMjMTf31/UkH4GROAlCMJbW79Div8+iwL35QZdu5fHvbYvVS1h7q4X/PxQQ2KpMqRYlcjp1K5jCglPKRt5FdMXzzB6GY1OVhY9e1bC3b0+AJqsLKJOniTM15eo48eRSKB8ZRk12oB145ooG4whuWIHkOrkzzQzE7MxY9APDiZp6tTPOui6cuUKZcuWpUePHsyaNeuNgVdQUBD9+vXDwMAAAFNTU9atW/fGqX5iY2NRKBRIJBL27t2Lh4cHVlZWQM4ccGPHjmXIkCG4ubkRFBTEhg0bkL4a3ODg4MD69etfC7r+7MWLF9py/Prrr+zevVu7z9vbm0ePHhEQEIBMJuP58+e0bduWQYMGER4ezk8//YS+vj56enraNA4fPkxgYCAKhQIbGxsmT57M4cOHOXv2LCqVitjYWPr27cuZM2d49OgRY8aMoXnz5to8r127xrp16/KVsX///vmOuX79Oh4eHgA0btyYNWvW5Au84uLiSE5OxsvLi5SUFNzd3WnatGmR90H49xKBlyAIb8V/v/6riUllBTYhflE5k57tc2q4UtVwOV7BuVgF52J0uRInI8uwFHyRhXHMS8qGXsPkxTOMo1/Qp1sF3N0dgDL50lPFxPB42zbC/f1JffIEfTN96jbR4YtaamSOLUmp9zVxZRoW3FdLpcL8q6/QO3yYpB9+QDly5Ae4I+/OtIBmTlX37qQPHQqpqZi6uLy2P33AAFQuLkhiYzEZOjTfvsT9+wRjaI0AACAASURBVN8q3+DgYJydnbG1tUWhUHDz5s0Cj8utbYmJiaFMmfzPw8TEpMBzVq5cia+vL1FRUdjZ2TF79mwAnj17lm8QFeRMkJ2enk52djbp6emvpZm7gsmfTZgwgYyMDGJiYmjUqBFjxowBckaNLliwAD09PXx8fLhw4QIlSpTgxYsX+Pr6kpmZSffu3Rk0aBDr1q1j+PDhNGzYEH9/f8LDw0lMTGTDhg1s2rQJQ0NDlixZwr59+9DX1yc1NZXFixdz7NgxduzYwdq1a7ly5Qo7d+7MF1Q5OjqyfPnywm49kDM/pZGREQAGBgb55q6EnGlHXFxc6Nu3L8nJyXz11VdUr14dc3PzItMV/p1E4CUIQqEK6rfl45WQrwnR3/82u4PCSC5RkqXXyzA7ugwpJUqi0dGB7GyMYl+S9dt9uBfO7MHlGDa8ClDq1U9+Go2GuIsXCfPzI/LAATSZmZSqZkXTHlLsqmSSUb0XynqjUFtWfe3cvPR370bv8GESvb1J/VOw8rlJSkri/PnzxMfHs2vXLlJSUti9ezf6+vpkZmbmOzZ3ofBSpUoRHR1N5cqVtfuuX7+OhYUFNjY2+c7JbWo8d+4cq1atomzZsgCUKFGC58+fU6VKFe2xSqUSuVyOVCrF2NgYpVKJoaGhdv+pU6eoX79+vm3wR1Pj6tWref78uTYgMTc3x9vbG319fR4/fswXX3wBQMWKFZHJZNr+UgBhYWFUr14dgJo1axIeHs6zZ8+oUKGCNr/atWtz8eJFqlevri23kZERtra2SCQSjI2NycjIyFe2t6nxMjQ0JDU1FV1dXVJTU7VBWC5LS0t69OiBTCbD3NycKlWq8PjxYxF4faJE4CUIwmtyA668neSd6qiws4pkr98xdvtLSSlRksRSZXhqUAEGtAC5DLKzMYyLofStG9oaLdmrL/eegyvh7l6lwPwyU1J4uns3Yb6+JN25g9zIAIemJahl/wzTMumk1vAktvZwso3LFHj+n6W5uKC2tyezUaP3c0PekyJrqAwMityvsbR86xquvA4fPsyXX36prSVKT0+nT58+uLi4cPLkSW2A8Pvvv2NnZwdA165dWbVqFXXr1kVfX5/4+Hh++uknvL29C82nSZMm3LhxAx8fH7y9venZsyfz5s2jRo0aWFpaolarWbJkCT179gSgc+fObNy4kTFjxiCRSAgNDWXZsmVs27at0Dw8PT0ZO3Yse/bsoWPHjmzYsIE9e/YAMH78eO1xBfWTsrW15caNGzRu3Jjbt28DOasUhIeHk5aWhr6+PlevXqVcuXKFplGQt6nxqlmzJufOnaNr166EhITg6OiYb/+lS5fYvXs3CxYsIDU1lUePHmmfhfDpEYGXIAhaBQVcPdun0c85DZ8dz1h5PBEat0NSqTwamQw0GgxjY6ib/YzhDY1oZJGBiVwDlHz1U7TEW7cI8/Pj6e7dqJVKzKuUo1nfslSziURqZoSyzv8RXXMgGt2Cm6DykiiVmE6aRPKkSWT9A4Ouj+XAgQNMnz5d+7uenh6tWrVCpVJhYGDAoEGDMDAwQC6X4+XlBUCNGjXo1q0b48ePRyaToVKpGDlyJJUqVSoyryFDhjBkyBDOnTtHkyZNGDlyJDNmzCA7Oxu1Wk3Lli1xdXUFwNXVlXXr1uHp6amtnZo3b16hs30DSKVSpk6dyujRo2nRogW1atVi6NCh2j5bMTExhS759O233zJjxgy2bt2KmZkZCoUCMzMzhg0bxtixY5FIJNjY2DBq1CiOHTv2rre5SIMHD8bb25vg4GBMTU35z3/+A8CKFSto3bo1Tk5OXLhwgREjRiCVShk5ciRmZmbvtQzCP4dEo9FoPnYh/oqMjAyxVuO/2Kd6XfDvu7aCmhMb11ZRt2kGj+TRnI/VJbmkNdmvvhBLZyXzZSUJTlYZNLbIwEzxbv+FZKlUPDt4kDBfX+IuXUKqq4tt8+rUqvSM0iZRZJlXJKXeKNKq9QaZ3psTBCTJyVi4uyO/fJmE1atJ//LLdypT3mf2PtdqvHnzpliJQxA+Q1FRUdqm7z8TNV6C8JnLnQbC1i6L8tXUpJdL52ItXULkxoAxaKIodf8uJi+eMayFJQN7vl1z358pIyII37KFx9u2kREXh6GdLXUHt6Rmyd8xkFwlo1Q94uv/hKpiR5C8/TI+ksRELNzckF+/TsKqVe8cdAmCIBQnEXgJwmfo6/9L5MglS9QKXVRKOVhD6JevmniepcKZW1QhEZMXz+nXxQb3UQ6A5TvX5mmysnhx/Djhfn5E/forEqmU0q2bUb2BLvaSU0izHpNeoT0x9UaTWdgIxSJI4uOxHDAA2Z07xK9di6pTp3c6XxAEobiJwEsQPgN++/RZFiAlJlVDlkIXdfSr5jRLkBioMbKKptTJW5i8eI4iPe3VPFo1gBp/Kb/0ly+1U0GkPX2KnrU1DiNcqVH5JZaxxwAd0qr2Qll3FGrLgjvcvxWFgmwzM+I3bkTVtu1fT0cQBKGYiMBLED4x/vv1WeWvITpBjVqheBVoveorVQ4kWWrkVkpq10pk7fc6WOtlAxLgi1c/f41GoyH2wgXCfH15dugQmsxMrJo2pc7ovlQxuoR+ZADZSUYo645EWXs42UZ/vS+V9OVLNPr6aIyMiNu+vdjWXRQEQfi7ROAlCJ8AjQbuJstYstOQ/RtzZhsnZ1T8q0ArFTOTCEZ0imWMW8VXZ0mA7L+dd2ZyMk927SLMz4/ku3eRm5pScZAHVZvbUOblbuQvF5GVWZKkpv9Hak0PNLoFT8T5tqTPn2PZty/qChWI37JFBF2CIPyriMBLEP4l/P1vs3fvAwA0wFNNXWLSK6NWKFArFDlL5jx5dXDlCPp3TuFbZ0tsDHKDK9NXP+9Hwo0bhPv58WTPHrJSUzFzdKSOzxwqV07D9NYmZLeeoDa3J6HtglcjFHX/dp7Sp0+x7NcPaUwMKWIRYUEQ/oVE4CUI/2C5wZYGCHmUAVXssGzqQMJLG7JO5AQykjJZyFUqdDIykOmpKKm4y1ft1Lj3d+B91GjlpU5PJ2LXLsJ9fYm7fBmpnh423btTcUAPbDSXMLzmgzQknozS9YhrMRNVxQ7vNEKxKDoREVj07Ys0MZG47dvJrFv3vaT7ufD39ycwMJCdO3eiq6uLt7c37dq10y5wDeDs7ExwcDAAp0+fJjAwEACVSoWrqyutW7fOl6a3tzf37t3DxMQEjUZDYmIiLi4u2rUgL1++zObNm9FoNGRmZtK6dWv69++PRCIhOzubLVu2EBISgo5OzjqbEyZMwP5Pa2r27t2brVu3amegf1f37t3jzJkzDC1kBYPff/8dIyMjKlWqxNSpU5kzZ85fyqe4hYSEEBUVRfcClqH6uzZu3Mi5c+fQ0dFh3Lhx2hn/c126dIlVq1aho6NDgwYN8PT0JCQkBH9/fyCn28H169fZsmWLdiLYHTt2EBcXx6hRo957ef9tROAlCP9AGg0s2RaOT5ASHBojr2kPBjnLmmTeyCbrRE4w4zUuiXF9lX9qbav8Wnp/lzI8nLAtW3gSGIgqNhajihWpMXMmFTo2xvzhNgx+G4JEnU56xQ6k5I5QfJ80GsxGj0aakkJsYCDqWrXeb/qfgSNHjtC2bVuOHTv2xkWyQ0ND2bFjB/Pnz8fAwIDExEQ8PT2xs7OjQoUK+Y7NXTIIcpYncnd3p0uXLoSFhbF8+XLmz5+PlZUVarWaBQsWsHXrVtzc3AgICCAxMZEVK1YglUq5ffs2U6ZMYdu2bW9cKPtdVKlSJd+yRX924MAB2rVrR6VKlf41QReQL2B+n+7evcvVq1dZt24dUVFRfP/992zYsCHfMStWrOCHH37Azs6O0aNH8/DhQxo3bqwtU0BAADVr1sTOzg6VSsXcuXO5desWrVq1+iBl/rcRgZcg/ANoNPAkTYezMQoCLqVz7aoZWQ9KgxR0HmRj8kSDqVyNiTyb368rgNfXTHzvZcrK4sWxY4T5+hJ98iQSHR1su3Wj7IABlKpigvGVVejtmwkSHdKq9c5ZQ9Hi/Qd9AEgkJCxahCQjA3UhkxIKhbty5Qply5alR48ezJo1642BV1BQEP369cPAIKe/oKmpKevWrcPY2LjI82JjY1EoFEgkEvbu3YuHhwdWVlYAyGQyxo4dy5AhQ3BzcyMoKIgNGzYgleb8EeHg4MD69evfKuhKTk5m1qxZKJVKsrKy8PT0pF69epw9e5b169djaGiIsbExlSpVok6dOuzbt49Zs2bh7e1NZGQkGRkZuLi4YGNjw4ULF7h37x52dnaMGDGC4OBgbt68yeLFiwGwsrLiP//5T74at169emFra4utrS0uLi74+PigUqnQ1dXFy8sLa2trNm3axOnTpzEzMyM9PZ0RI0Zw9epVQkNDSUtLY+rUqVy6dImjR48ikUho164dffv25eTJkwQEBCCTyShVqhTTp0/nxo0bLFu2DJlMhrGxMT/88AMnT54kIiKCUaNGsW3bNo4dO4aOjg61a9dm9OjRbNiwgWfPnpGQkMCLFy/45ptvaNSoEd999x1paX/8v2FnZ8ekSZO0v1+/fp2GDRsikUgoVaoUWVlZxMfH51s3skqVKiQlJaFWq1GpVNpnCBAdHc3hw4dZv349kFNb2qlTJ+rXr09ERMQbn+3nQARegvCRPE3V4VysgnMxCs7GKohMe/VxvJwOp3JGIdqUSaJcSd2cfvCv5C7j86GCrvToaB5v3ZozFcSzZ+iVKkW1b7/F1sWFcvpRZP86F90r/yNbYYyy7lcoaw/7WyMUiyK7cwe94GBSJk0iq/IHCuqKyY4dd9i69fZ7TdPV1YH+/au98bjg4GCcnZ2xtbVFoVBw8+bNAo/LXZ8wJiaGMmXyT5RrYlLwoIiVK1fi6+tLVFQUdnZ2zJ49G4Bnz57h7Oyc71hDQ0PS09PJzs4mPT39tTRNTd+uD6Kvry8NGjSgX79+vHz5klGjRrFjxw4WL17MmjVrsLCw0C7Lk0upVHLlyhU2bNiARCLh4sWLVKtWjUaNGtGuXTtKlfpj0XYfHx9mzpyJnZ0de/bsITw8nKpV/1iYPTo6mk2bNmFqasr06dPp06cPTk5O/Pbbb6xatQo3NzdCQkJYv349arWagQMHas+1s7Nj/PjxhIWFceLECVatWoVEImHcuHE0bNiQY8eO0b9/f9q1a8fPP/+MUqnk9OnTtGrVChcXF86cOUNycrI2vYcPH3LixAnWrFmDjo4O//d//8fZs2cBUCgULFy4kIsXL7J9+3YaNWrE/Pnzi7y3SqUy33MwMDBAqVTmC7wqVqyIl5cXJiYmVKpUCVtbW+2+7du3079/fxSKnD8QTUxMaNSoEQcPHnybR/tZEIGXIBSTZ2lSzsXocjZWwflYBRGpOR8/g+wM9CIi4IgSYixAWhbIW6Ol/OBl02g0xJw/T7ivL89+/hmNWk2J5s2pOXs2pdq2xiDsZ4xODkL+8iZZhtYkNf2e1JoD//YIxaLIQkOxHDAAja4uqYMHk12ixAfL61OWlJTE+fPniY+PZ9euXaSkpLB792709fXJfLWAea6srCwASpUqRXR0NJXzBLvXr1/HwsICGxubfOfkNjWeO3eOVatWUbZszvtbokQJnj9/nq+ZT6lUIpfLkUqlGBsbo1QqMTQ01O4/deoU9evXz7etIOHh4XTo0EGbj6GhIS9fvsTAwAALCwsgZ/HquLg47TmGhoZMnDgRHx8flEolHTt2LDT9uLg4bd+kXr16vbbf1NRUG5w8evQIPz8/AgIC0Gg0yGQyHj9+jIODAzo6Oujo6FCt2h/Bcfny5bXnvXjxgnHjxgE5tXiRkZGMHTuWLVu2sHfvXmxtbWnRogUeHh74+fnxzTffUKJEiXx9rh4/fswXX3yhrSl0dHQkLCwMQHvvra2tycjIAHhjjZehoSGpqana31NTUzEyMtL+npyczJYtW/D396dEiRKsWLGCbdu24ebmRnZ2NufOnWPkyJGF3ltBBF6C8MG8SJdyLkbBuVhdzscqCFPmfNzM5Nk0tsxgeAUl8SF3WPTdL6RqwKTKCDL0SlDniw9bo5VXZlISETt3Eu7nR/L9+8jNzKg4bBgV3N0xLl8a/ZvbMAxoiSzpCWrzSqh7rOFl2Q7vZYRiUeS//46FiwvZRkbE7dz5SQRd/ftXe6vaqfft8OHDfPnll4wZMwaA9PR0+vTpg4uLCydPnqR58+ZATifz3GCja9eurFq1irp166Kvr098fDw//fQT3t7ehebTpEkTbty4gY+PD97e3vTs2ZN58+ZRo0YNLC0tUavVLFmyhJ49ewLQuXNnNm7cyJgxY5BIJISGhrJs2TK2bdv2xmuys7Pj2rVrVKlShZcvX5KcnIylpSWpqanaZrGbN2/mW3czJiaGu3fvMmfOHFQqFb169aJjx45IpVKys/MPQrGysuLJkyeUK1cOf39/ypUrR8uWLbX78zatlS9fHldXV2rWrMnjx4+5evUqFSpUYNeuXdrFwe/du6c9PrdWsXz58lSoUIGFCxcikUjYvn07FStWZP/+/QwbNgxzc3N8fHw4deoUqampdOnShTFjxuDn50dQUJB2DVBbW1u2bduGWq1GR0eHa9eu0alTJx48eFDgvXtTjVfNmjVZuXIlLi4uREdHo9Fo8i3Yrauri4GBAfr6Oeu7WlpakpCQAOQEk+XLl//LAyE+FyLwEoT3JDpdyrlYBVfu6nAisgSPXgVaJrKcQGuwnRInywyqm6jZGqTPah8Njx5ag/UgKtqbEpNkSp3KmexeHveGnP6+hOvXCfPz4+nevWSlpWFepw51Fi3Cpls35JpUDK5txPDYZqTp8WSUbkBcy1moKrTH0qoEfOAFwOW//YaFmxvZ5ubE7dxJVrlyHzS/T92BAweYPn269nc9PT1atWqFSqXCwMCAQYMGYWBggFwux8vLC4AaNWrQrVs3xo8fj0wmQ6VSMXLkSCpVqlRkXkOGDGHIkCGcO3eOJk2aMHLkSGbMmKENQFq2bImrqysArq6urFu3Dk9PT2QyGTKZjHnz5iF/tRh7XnlHwnXo0AEPDw9++uknfv31V1QqFV5eXsjlciZOnMikSZMwMjIiOzubcnnendzlrgYPHoy+vj4uLi7IZDKqV6/O6tWr8zWtenl58dNPPyGVSrG0tKRfv36FXvOYMWNYsGABGRkZqFQqxo8fj729PU5OTnh6emJqaqq9vrwqV65MvXr1GDVqFBkZGVSvXl1bmzV+/HhMTEwwMDCgadOmPH36FG9vb/T19ZHJZEyePJmrV68CYG9vT9u2bRk1ahTZ2dnUqlWLFi1aFBp4vUm1atVwdHRk5MiRZGdnM3HiRCBnhOq1a9cYOnQoY8aMYcKECSgUCoyMjPj+++8BiIiIeK2JWnidRKPRaD52If6KjIwM7Zpx77p+3L/Jp3ptn8J1xaiknH/VR+tcrIL7KTlfGMZyDY3MVTSxyqCJpYovTNXoSHJmlN97VJ+oqFQePXvVXyItnIr2plhb53Ri/pA1XVlpaUQGBxPm50f8lSvo6Olh07MnFQYNwqxWLXQSH2N4ZTUGN3cgyUonvWJHUuqNyjdCsTiem+7PP2M8dy5xW7eS/arZ6kPLe115a0n+rps3b2prJoQPz8/PjwEDBqBQKJg5cyYNGzakc+fOxV6O+Ph4fv31V3r16kVGRgbu7u4sXbo0Xz8y4dMWFRXFF4UMBBI1XoJQhLyTlmbq6pJkXZqk0mVILFWGNPOcviTSzAx0zyShe1eOLEOFNCuLi9nZXAQW50krKfNVdX3acyCRitYRfDVKjbu7A5D+wa4hJSyMcD8/HgcGkhkfj1GlStScNYtyffuiMDVFFnUdo5+/Qu/+gZwRig59UNb96sONUCyEJC4OjYUFqs6dUbVrBwXUfAhCUQwMDPD09ERPT49SpUrR9iOt32lqasrt27cZNmwYEokEZ2dnEXQJWiLwEj4beYOot6FWKLiUoAdVa2FQpzKpFpYASDMzMY5+QYlH9zF58RzDmJfcjumKUm2EriwFpAUvYWMif4aV/gOsS915tQi1w3u5roJkq9W8OHqUMF9fXp4+jUQmo3TnzlTw8MCqSRMkgCLiFEbHV6L75EyeEYrDyTYq/i8IxcmTmI8YQcKaNajatBFBl/CX9OnThz59+nzsYiCVSrXNb4LwZyLwEj4L/v638fL6HwBOTgU3JakVCpJKltLWaKVaWIJEgkyTRd0SappaJtPESoWjWSYKqQwoD5THf78+Xj5mONVRsXu55A3NcZX5EBOc5kqPiiI8IIDHAQGkPX+OfunSVPvuO+xcXdGztoZsNXp392J0eSXymFtkGZYiqdk0Umu4f9ARikXRPXoU8xEjUFeuTIaj40cpgyAIQnERgZfwr/OuNVcA588/B8DHp7m2pik5U8KFOIV2Lq0biXKykaAr1VDfPAMnqxSaWqqobZbJzgP67A3Q5zSK19O+mjOCp2f7Dz8KsSAajYaYs2cJ8/Pj+S+/oFGrKdmyJbV+/BHrdu2QymRIMlPR/309hlfWIkt+SqZFZRLa/Ze0qj0/+AjFouj+/DPmX31FZvXqxG3diibPXEGCIAifIhF4Cf9IRQVXuUFUYTVXBXFyKk2XnlUp26Em3rdy5tG6nignSyNBIdVQ1yyD8VVSaGqZQR3zDPR08p+/96g+N+/L+aJy5utpf+AJTQuTkZjIk507CfPzI+XBA+Tm5tgPH47dwIEYvVrWRZoag8GljRhe980ZoVimIXGtvFFVaPfe1lD8q2S3b2Pu6Ulm7drEBQSgKWSCTkEQhE+JCLyEYufvf5sDBx6/NnljXkUFV05Opd+qj1SqWsKleDnnYnQ5F6vgPwlysi5IkEs01DHPZGylFJpYZVDPPAN9nYLTyB2JmBt0FcdUD2+ScP06Yb6+OVNBpKdjXq8edZcsoeyXX6Lzam4dnYRwDK+sweDWqxGK9p1IqTuKzDINPnLp/6CuVo2kH38krVcvNHkmaBQEQfiUicBLKFZv09cqd9+7dkBPy4LftE2HuvyeICdTI0Em0eBolsnX9kqcrFQ0MM/EQFb4LCq5wRb80YyYW6v1sahTU4kMCiLMz4+E339HR18fm969qeDhgVnNmtrj5FHXMLy8Er0HB0EqI61aH1LqjiSrmEcoFkV/924ya9RAXbUqqR4eH7s4nw1/f38CAwPZuXMnurq6eHt7065du3yLLTs7OxMcHAzA6dOnCQwMBHLW23N1daV169b50vT29ubevXuYmJig0WhITEzExcVFuxbk5cuX2bx5MxqNhszMTFq3bk3//v2RSCRkZ2ezZcsWQkJC0NHJ+ctnwoQJ2Nvb58ujd+/eWFtbI5VKUalUVKtWjTFjxrzTJJ0hISFERUXRvXv3AvdPnTr1by2Q/fDhQ5KTk6ldu/ZfTuNtHTx4EBMTE5o3b86uXbvo06cPBw8e1K7b+DZGjBjBrFmz3mnqlKSkJEJCQujQoUOB787buHXrFj/++CPNmjXLV9b9+/fTtWvX97o4el5Pnz7lxx9/BHKWO/r222/zTYJ78OBBfv75ZyDnXX/w4AFBQUGo1Wrmzp1LcnIy2dnZTJs2DRsbG3bv3s2hQ4eQSCQMGTKEpk2bvlN5ROAlfHB5mw1za7JWrOhEz57l/1a66VlwJT5nncPzMQquJCjIyJagI9FQyzQTT3slTS1VNLDIxPBVoOW/X5+lR4uuXckbbH2sZsRcKQ8fErZlCxGBgWQmJGBcuTK1vL0p16cP8tymOY0mZ4TibyvRfZo7QnHUqzUU/1lD2A38/DCdMoXU3r1JXLbsYxfns3LkyBHatm3LsWPH3rhIdmhoKDt27GD+/PkYGBiQmJiIp6cndnZ2VHjVjJ0rd8kgyPlydnd3p0uXLoSFhbF8+XLmz5+PlZUVarWaBQsWsHXrVtzc3AgICCAxMZEVK1YglUq5ffs2U6ZMYdu2ba99AS9atEgbaPn6+rJ27VrGjh371tf+pgDh7wRdACdPnsTCwqJYAq+8z87X17fYRnE+ePCAM2fOaJdq+isuXrxIjx496Nu3b77tfn5+dOrU6YMFXkuXLmXEiBHUrVsXHx8f/ve//+VbiaBr167a+7pw4UK+/PJLjI2N8fb2pkOHDrRt25bLly8TERGBkZERe/bswdfXF5VKhbu7O02aNNGuSPA2ROAlvHd/7p+Vt9kwtyZr+PA67zwRpyoLrib80Rn+crwCVbYEKRpqmmYyrIKSJpYZhJ3V4ecdelxBzhXyT0uQN6gqzMcOtrLVal4cOZIzFcT//odEJqNMly5UGDQIy8aN//iAZ2Widz/4TyMUp78aoWj8UcpeFIP16zGdMYP0du1IfMOyJcL7deXKFcqWLUuPHj2YNWvWGwOvoKAg+vXrh4FBzsS+pqamrFu3DmPjot+r2NhYFAoFEomEvXv34uHhgZWVFQAymYyxY8cyZMgQ3NzcCAoKYsOGDdqaBwcHB9avX//GL98BAwbg6urK2LFjuXr1KmvXrkUqlVK2bFm8vLzIysrixx9/5MWLF6jVaiZOnMjjx4+JiIhg6NChTJ8+HaVSiUqlYvTo0dStW1db03fv3j0WLVqEVCpFoVAwefJkNBoNP/zwA9bW1kRGRuLg4MB3332nLc/Lly85dOgQcrmcqlWr8tNPP1GuXDkUCgXfffcdc+bMITExEfijRu/EiRNs374dHR0datWqla/25969e6xbt4758+dz9OhR/P398fX15dq1a/zyyy9YWVlhYWFBUlISSUlJLFiwAAcHB27evMn48eNJSEigZ8+er9XurVmzhgsXLlCyZElteVJSUgosX9++falevTr/z96Zh0VVv238MyvMDDuoqCjIizvuW2qmpmVaWpaGoomYSxqW/nLN1DRCUdPMBRNRUdTccS3L0qzUNBVFsywWUQSMHWZghmHO+8fABLKI5u75XFeXzcxZvuecYc59/aworAAAIABJREFUnu/zPHdiYiKenp5MmzaN8PBw/v77b/bs2QOYo1SbNm1Cq9UyadKkUv6RRqORoKAgEhMTMZlM+Pj4UKtWLfbt24dCoaB69eoW4bNv3z7S09OZPXs2AH5+fjRu3JhBgwYxduxYunbtyoQJE5gxYwZnz55l27ZtKJVK3NzcmDp1Kj/99BM7d+4sdazjxo0rNZ4///yTVq1aAdCxY0dOnTpVSngVc/nyZeLi4vjggw8A8wOIl5cX77//Pq6urkyYMAGVSkV4eDhyuZykpCRsbGzuSHSBKLxE/gMVJcDfmp91N9OGAAYTRGX+m6P1W7qSfJMECQJN7YwM99DSycVAeycD9gqBiD0qVq7UVCquHraoqoy8pCSubt5M/KZN5Ccno6pVi8ZTp+I+eDDW1atblpMYtGYPxXNfIs9JpMCpAZkvLDFXKMrKVl0+CmhCQrD75BPye/cmIyQElI/mOO8nVpe2Yh29+Z5uM7+ZL/qmPrddbt++ffTt2xd3d3eUSiWXLl0qd7niG0hqamoZ6xe7CoofVq5cSXh4OCkpKXh4ePDJJ58AcOPGDfr27VtqWY1GQ35+PiaTifz8/DLbLDaergwrKysMBgOCIBAcHExISAiOjo6sXr2agwcPotPpqFmzJnPnziU2NpbTp09bTJ4TExNJT09n6dKlZGRkkJCQUGrb8+fPZ9q0aTRo0ICffvqJZcuWERAQwLVr11iyZAnW1tYMHDiQtLQ0nJ3Nff2qVatGnz59cHJyokmTJuTl5eHv70+DBg1YuXIlbdu2pX///ly7do2goCCCg4MJCwsjLCwMa2tr5s6dy6lTp2jf3uwQ0aBBA5KTk9Hr9Zw8eRIwm3b//PPPdO3a1XLt/Pz82LFjB5MmTeLAgQPIZDKWLFlCcnIykyZNKiW8YmNjiYqKYs2aNeTl5eHjY/7ObNiwocz4QkJCuHnzJkuWLMHNzY2ZM2dy7Ngx/Pz8iIyM5NVXXyU6OpqGDRsyfPhwDhw4wMGDB0sJncjISOzt7Zk1axZarZYRI0bw5ZdfWs5TSdHTt29f1q9fz5w5c/jhhx84efIk9vb2WFlZcfr0adq0aYPBYECpVBIWFsa6devQaDQsXbqUyMhIBgwYUGYK/FYEQbB8t9VqNbm5ueUut2HDBvz9/S2vk5KSsLW1ZenSpaxdu5aIiAhGjRqFXC5nx44dhIWFlYneVQVReIlUyO3aNlSUAH+3QqvABBeyFBxPVfJLqhWnMxTknZHCJVDLTTgoTNgrTNjJBeRSgQsouICCVWjM47klH+tRFFe3IggCqT//TGx4OMmHDiGYTFTv1o0W8+bh2rMnEtm/Wf9SXarZQ/H8eqT6TPS1OpDdLQh9vR4PvUKxUoxGrI4cIa9fPzKXLROboz5gsrOzOXHiBBkZGezYsYPc3Fx27tyJSqUqU+BSWFgIgKurKzdv3qR+/X9zAy9cuICTkxNubm6l1imeajx+/DghISHULrJ5qlatGklJSTRo0MCyrFarRaFQIJVKsbW1RavVotFoLJ//+OOPtG3bttR7t6LValGr1WRmZpKammrxodTr9bRr147MzEw6duwImPN5PD09OXDggOX166+/zuzZszEajWVumqmpqZbxtmjRgpCQEADc3NwsY3J2dsZgMFR6zuvWNadRxMTEcObMGb7//nvAfC2uX79OZmYmkyZNAkCn03Hjxo1S63fo0IFz585x8+ZNXnzxRU6fPk1UVBRjxoypUDQ3bNgQiUSCk5MT+fmlnTBiY2Np1KgRUqkUjUZjyaMrb3wANWrUsFxnb29vEhIS8Pb2LrO/4vNx6/6uXr1K27ZtAbPY9vDwIDExsdJzBtC5c2emTZuGg4MDQ4YM4auvvuLkyZN07tyZGzduUK9ePct1aNmyJadOneLIkSO3jXiVzOfS6XQWIV6SnJwcEhISaNOmjeU9e3t7nn32WQCeffZZvvzyS8tnAwYM4NVXX+WDDz7gzJkzpda7HaLwEimXqiTB363AKsZogugshWXq8FS6Em2R0FLJTdgrBPKumJdt0ariCkjLeB4jwWXIzCRh2zbiN2wgNzYWpaMjXmPG4PHWW2jc3UstK8uMQ3N2Nerft0KhHv3/vWT2UKzZ9iGNvooIAuj1YG1N+vr15ijXfcrheBzQN/WpUnTqXnPo0CFeeeUVAgICAMjPz2fAgAEMHjyYo0eP0qVLFwCioqLw8PAAzDkvISEhtG7dGpVKRUZGBkFBQQQGBla4n06dOnHx4kUWLFhAYGAg/fv3Jzg4GG9vb5ydnTEajSxdupT+/fsD0Lt3b9auXUtAQAASiYTo6GiWLVvGli1bKj2eTZs20aNHD+zt7alevTrz58/HxsaGn376CbVaTUxMDJcvX6ZLly4kJiYSGhpKu3bmat6YmBh0Oh2LFi0iNTWVd955p1RitIuLC3///TdeXl5ERUWVMtmuDIlEQknb4+Loiru7O7169eLFF18kIyODvXv3UrNmTapXr87nn3+OXC7nwIEDpQQuwHPPPcfq1avx8vKiQ4cOLFiwgDp16pSZhi1vn+VRt25dduzYgclkQq/XExcXV+H4wDx9WhzVi46OplevXkil0irvz93dnfPnz9O1a1e0Wi2xsbGVmmcXb9vOzg5ra2u+//57iwn61q1bmT17NjY2NsTHx5OXl4dKpeLcuXPUqVOH7t273zbi1aBBA86ePUvr1q05ceIErVu3LrNMVFSURSwW07x5c06cOMFLL71EVFQU9erV4+rVq6xatYqgoCDkcrnlQeJOeHp/BUVKUVFeVsmGo/+VQgEuZcn5Jc2K0+fkHDlYA320+QurkpmwUwho/zIv27JIaNVrZXxsxFRVyIiKMreC2LMHU34+Tm3b0mbiRGq9/DIya+tSyyqSo9CcDSldodjmHQodvR7S6O8AQcA2KAjlyZOkb92KUJQrJPLg2b9/vyUqBGBtbU23bt3Q6/Wo1Wr8/PxQq9UoFAqmTJkCmKMc/fr1Y8KECcjlcvR6PWPGjMHLq/Lvnr+/P/7+/hw/fpxOnToxZswYZs2ahclkwmg00rVrV3x9fQHw9fUlNDSU0aNHI5fLkcvlBAcHoygnIjpx4kSkUikmk4n69esTEBCAVCrl/fffZ/LkyZhMJjQaDTNnzsTb25t58+bx7rvvYjKZeO+994iNjQXMkau1a9fyzTffoFAoGDlyZKn9TJs2jcWLFyMIAjKZjOnTp1fpHDdq1IgVK1bgfstDk5+fH/PmzWPv3r2WKTdHR0cGDRpkGV95npLNmjUjISEBX19fvLy8SE5OZsiQIWX26+HhwZw5c8oIhltp0KAB3bt3Z+TIkbi4uOBY1Ki4vPEBKJVKFi9ezM2bN2natCnPPvssqampxMTEsHXr1tuej1dffZX58+czduxY9Ho9/v7+ln2WR/PmzZk0aRLLli2jS5culsrNDh06sHv3bkv07e2332b8+PFIJBLc3NyqXMUZEBBAcHAwq1atwsPDwyLUPvnkE0aNGoWrqysJCQllxOH48eOZN28eu3fvxsbGhtmzZ2NnZ0f9+vUZPXo0EomEZ555xpI/VlUkQkkJ+xhhMBgsydmVW7Q83tzvYysWXOVNG/5XP0GTAJey5ZxItWLrPhVXfpVTKJifklRygbw48/+3bWFAIf33a/i4C61br5lRpyNxzx7iwsPJvHABmVpNnaJWEPa3utcLAlZXj6I5sxKr679gUtqhaz7MXKGoqfGAj6QsVfo+CgK2H3+MTWgo2mHDyA4Kgjt8InzQlDyuOymxvx2XLl2iRo2Hf91ERO6Ekm1FRO6OlJQUmt76+16EGPF6irl1OvG/Cq0NkSo2f6Mmu0BKVoGUbKOEQlNROPqa+Z/6TQqwUwholHIKHAyPvciqjJy//iJu40aubd9OQVYWtg0b0jwoiDpvvIHi1uqwwgJUf+1F89tKFGmXKbSpSXaXWeiaDnkkKxQrxGTCbsYMNOHhaN9+m+y5c+EOK35EREREnmRE4fWUUlJ03e10oiDAlVw5n2/T8NOPVqTHFCWC1wErmYCT0pynZSc3YeUilBJZ5gjDw+8Cf68xFRQQt2sXF1asIPXnn5EoFOZWEMOH49y+fZm8CHOF4mZszn6JLPdGUYXi5+Q1fO2RrVCsDNsFC9CEh5M7diw5H30kii4RkccQMdp1fxGF11PCvcjhEgRYvM2GXd+pyC6QkFUgxWiSWKJZ1eoX0r2rnkk+ubipC+/5MTzK5N24QfymTVzdvJn8lBRUbm40mT6duoMGYV2tWpnlpbpU1FFhZg9FfSb62s+Q9fx89B7PP9oVirdBN2gQJjs7tGPHiqJLREREpBxE4fWUsHv331y6lEbTpubeM1WZWhQEiNXKOJ5qxaa9Ki6fVFBw1XwzVboLRe0dBOyamxj8ku6JnTKsCMFk4p9jx4jbsIHk775DMJmo8fzzdAkJQd2uXalWEMWYKxS/LKpQNJD/f73RthlLQc2qlyI/chiNqHbsIM/Hh0IPD7Tjxj3sEYmIiIg8sojC6wmjot5bxaJr586+5axlRhAgXidj8VYbfvzRiqwCKQW35Gh5NjYy4EUd7w/UPrUBDUN6Ole3bSN+40a0cXEonZzweucdcyuIunXLTUBXJEf966EoU5DXeKDZQ/FxqFCsDIMBh3ffRXXgAIW1amF47rmHPSIRERGRRxpReD1BVNZ7q2lTZ/r3L3uTT9DJ+CVVyYk0Jd99Y03WealFZDl7FZojWgoTKmeB/i8+uYnwt0MQBDLOnSNuwwYS9+zBpNfj3L49jT74wNwKojzDXkHA6uqRogrF45iUdmjbBhRVKFYvu/zjhl6P4+jRWH/3HdkffyyKLhEREZEqIAqvx5TyIltVydu6rpOyaKstR45akWWUYig0h63kUgFj0TRiy2YGBr+k463Xnk6RVRKjTsf13buJCw8n6+JF5BoN7oMG4TFsGPaNK5imLSxAdXkHmjMhJSoUZ6PzHoKgrNyg+7EhLw/HkSOxPnKErKAgdMOHP+wRidyGiIgItm3bxvbt27GysiIwMJCePXuWMpAu2Ubg2LFjbNu2DTB3hff19S3TqDIwMJArV65gZ2eHIAhkZWUxePBgixfkmTNnWL9+PYIgUFBQQPfu3fHx8UEikWAymdi4cSMnT55EVjQtX+wVWJI33niDGjVqIJVK0ev1NGrUiICAAItpdlU4efIkKSkpZfwLi5k+ffp/MsqOiYkhJyfngZhkV5UDBw6QkJDAm2++ybp16yyd8m+3jp2dHV26dGHHjh1VNuAOCQmhbt26FXqAXr16lYULF7J8+fI7OoaoqChsbGzw8vK66xYXFy9eZOnSpchkMtq3b2/pVVbMxo0b+fXXXwFz9/r09HT27dvH6dOnCQkJQSaT0a5dO0aPHg2YDbcvXLiARCJh/PjxNG/e/I7HJAqvx5CKIlvl5W3dyJNyIs2K8EgV0SeU6Av/TYZ38irEzlrAXmFCLRPA6fHvoXWvyPnrL+LCw0nYsQNjdjZ2jRvTYt483N54A0U5dhMAEkMu6oubUVwIwyHrGgXODcl8cSl5DV59LCsUK0Nx8SJWJ06QuXAheeU0dhR59Pj222/p0aMHhw8fvq1JdnR0NFu3bmXhwoWo1WqysrIYPXo0Hh4e1KtXr9SyxZZBYLacGTp0KH369CEuLo7ly5ezcOFCXFxcMBqNLFq0iM2bNzNkyBA2bdpEVlYWK1asQCqVcvnyZaZNm8aWLVvKdGhfsmSJRWiFh4ezevVqxo8fX+VjLykuy+O/iC6Ao0eP4uTk9EgJr2KcnZ2rJLqAUt+L8PDwKguv+8X+/fvp2bPnbRv3VsbChQv59NNPqV27NpMmTeLPP/+02B0BvPXWW7z11lsATJ48mXFFOaorVqxg9uzZeHh4MG7cOGJiYjCZTERHRxMaGsr169eZPXs2a9euveMxPTDhZTKZ+Pjjj/nzzz9RKpUEBgaW6vK7d+9e1q1bh1Qq5Y033rB0NxYpS3Gkq7zIVnK+lF3XlRxPs+LQN1aknStK8C4SWx6NjNg1M+H7ko5hYkSrFCaDgaRvviFuwwZSjx9HqlRS65VXqDdsGE7t2lVokSHV/mP2ULywHqk+C5PHc2R0DSqqUHzCEuFMJgAK2rXj5i+/YLqHzUZF7h9nz56ldu3avPbaa8ydO/e2wmvv3r28+eabqIscB+zt7QkNDcX21v5zt5CWloZSqUQikbB7926GDRuGi4sLAHK5nPHjx+Pv78+QIUPYu3cvYWFhFruVxo0bs2bNmjKi61YGDRqEr68v48eP59y5c6xevRqpVErt2rWZMmUKhYWFfPrppyQnJ2M0Gvnf//7H1atXSUhIYMSIEcycOROtVoter2fcuHG0bt3aEk25cuUKS5YsQSqVolQqmTp1KoIgMHv2bGrUqEFiYiKNGzdm8uTJlvH8888/HDx4EIVCQcOGDQkKCqJOnToolUomT57MvHnzyMrKAv6N6P3www989dVXyGQymjdvXuUO7CWjlCdPnuTw4cN89NFH+Pj4WLrdOzk58emnn1rWSUpKYtasWYSGhvLWW2/RsmVLYmJiqFu3Lk5OTkRFRaFQKPjss88IDw/HycmJ7OxssrOzWbRoERMmTGDhwoVcu3YNQRAYNWoUrVu35siRI4SHh+Pg4IDRaLT4UxaTmprKnDlzEATBYigOlHvNDh06xM8//4xWqyUrK4vhw4dTs2ZNfv31V65cuYKHhwcFBQV8/PHHpKSkYGdnx6effkpkZCRHjx4ttd+PPvoIV1dXwOzrWVBQYOl836FDB3777bdSwquYo0ePYmtrS4cOHQBzt//s7GyMRiN6vR6pVIqzszPW1tYYDAa0Wq0lUnunPDDhdfjwYQwGA1u3biUqKor58+dbDEgBFixYwP79+1Gr1bz88su8/PLLVXKqfxq4dVrx0qU0OnasydChjbmZL+VEmpLjaWZj6dhf5HAJZBKBwgTzTb95MwNqZ4HXn+IcrcrQJSaaW0Fs2oT+n39Q16lDkw8/xH3wYKxK/GDciiwj1lyheHnbvxWKbcdh1/QF9E+gk4IkJwf5m2+i8vEh7403RNF1h8Rv3Ur85s33dJsevr54+Nze/3Hfvn307dsXd3d3lEplhUbLxQ8XqampZexT7Ozsyl1n5cqVhIeHk5KSgoeHB5988gkAN27coG/f0sU8Go2G/Px8TCYT+fn5ZbZZld98KysrDAYDgiAQHBxMSEgIjo6OrF69moMHD6LT6ahZsyZz584lNjaW06dPW0yRExMTSU9PZ+nSpWRkZJCQkFBq2/Pnz2fatGk0aNCAn376iWXLlhEQEMC1a9dYsmQJ1tbWDBw40OJjCGYz8D59+uDk5ESTJk3Iy8vD39+fBg0asHLlStq2bUv//v25du0aQUFBBAcHExYWRlhYGNbW1sydO5dTp07Rvn372x57Rdy4cYMvvviCGjVq8M4773D58uVyl9PpdLzwwgt88MEHDB48mPHjxzN69Gjeffddi60SmK2EduzYwaRJk9i9ezf29vZMnz6drKwsxo0bx6ZNm1i5ciVr1qzBzs6u3IjaV199xQsvvEC/fv04fPgwkZGRFV4zmUyGTqfj888/JzMzk5EjR7Jt2zY6dOhAz549cXV1RafTMWbMGGrWrElAQABXrlxhwIABlUblbjVhV6vVZQzJi9m4cSNz5syxvPb09GTKlCnY2dnh5eWFu7s7Wq0WqVSKr68vWq2WqVOn3vbalMcDE15nzpyxmLG2bNmSixcvlvq8YcOG5OTkIJfLEQShUgPOp4WIiMvs33+VY8fMPw4dO9akwMoa1z5toVNjuh5x4a9cs6+ZjdyE25+F8I153XYtDUicxanDihBMJm4eO0bc+vUkHz4MgkCNHj2o5+dHjW7dym0FUYwi+VxRheJBkCnRNR6ItvUYCh3/r8J1HnckmZk4DRmCJDoawc/vYQ9H5A7Izs7mxIkTZGRksGPHDnJzc9m5cycqlYqCgtLm84WF5v57rq6u3Lx5s5R584ULF3BycrJED4opnmo8fvw4ISEh1K5dGzALkqSkJBo0aGBZVqvVWkyFbW1ty9wYf/zxR9q2bVvqvVvRarWo1WoyMzNJTU21+FDq9XratWtHZmYmHTt2BMw3T09PTw4cOGB5/frrrzN79myMRiMDBw4ste3U1FTLeFu0aGEJDri5uVnG5OzsjMFgqPScF0d/YmJiOHPmDN9//z1gvhbXr18nMzPTIlZ0Ol0pMaDT6Syeme3atcOvgr+3km5/9vb2Fmuq6tWrVzq+4miPjY2NZdrY1ta2wnViYmI4f/48v//+O2D+jqSnp6PRaCxCuVmzZmXWi4uLo1evXoDZizEyMrLCa1a7dm1atWqFVCrFyckJW1tbMjMzS23Pzs7OYufl5OREfn4+O3bsqDTipdFo0Ol0ls90Op1FhN86VhsbG8t3Oycnh40bNxIREUG1atVYsWIFW7ZsQalU4uTkxOLFi9HpdIwdOxZvb2+qldOrsTIemPDKzc0tdcAymQyj0WgJK9evX5833ngDlUrFCy+8UOHTVcn1i5845HJ5qVDm48SaNefYuvX3cj87diwBNCqaDOlCtWebkOpUnUuZ5rC8Ri7gflGg3gUBe6WArQJ+Om0WYSvmGBnpUyxc1UX/PVo8rGuWn5rKlfBw/lizhpzYWKyrV6fFpEk0fPttbD08Kl5REJD8dQjZz58hjT+GYO2A6bkpFHYYh8LWFYcSiz7O38dySUtDPmQIkkuXELZvR9OnDxXfFh9PHsQ18/DxqVJ06l5z6NAhXnnlFQICAgDIz89nwIABDB48mKNHj1oeiKOiovAo+ht4+eWXCQkJoXXr1qhUKjIyMggKCiIwMLDC/XTq1ImLFy+yYMECAgMD6d+/P8HBwXh7e+Ps7IzRaGTp0qX0798fgN69e7N27VoCAgKQSCRER0ezbNkytmzZUunxbNq0iR49emBvb0/16tWZP38+NjY2/PTTT6jVamJiYrh8+TJdunQhMTGR0NBQ2rVrB5hFhE6nY9GiRaSmpvLOO+/QuXNny7ZdXFz4+++/8fLyIioqijp16lTpHEskklJCqDhw4O7uTq9evXjxxRfJyMhg79691KxZk+rVq/P5558jl8s5cOBAKYGrVqsrTEJXKpWWVjVXrlwps797SfHxuLu7U61aNfz8/NDr9YSHh1tEc0ZGBo6Ojly+fLmM+Khbty4XL16kfv36lghcRdcsOTmZP//8E4D09HR0Oh2Ojo4WY/SKjvF2ES+NRoNcLuf69evUrl2bX3/9tUxyPcBvv/1mEetgjqqq1WpUKhVgFtuZmZl4eHigUqmQyWSo1WqUSmUpYVdVHpjwsrGxQavVWl6bTCaL6Prjjz84evQo33//PWq1msmTJ/P111/Tu3fvCrdXWFj42Jtkl5ckb1QqyXatSZZrLdS9+6FzcuZ3QCUz0V5RwPRGejq5GLj4o5zpX5lv9x1bGTAaoWMrc4Srf888HvXT8SCvmSAIZJw5Y24FsW+fuRXEM8/QdtIkavXpg1SpxADlj6ewANWVPWjOrESR9kdRheLH6Lx9zRWK5hUf2rHdd3Q6XPr1QxITQ8a6ddj06fPkHFsJ7pdJ9qPA/v37LREGAGtra7p164Zer0etVuPn54darUahUFgiLd7e3vTr148JEyYgl8vR6/WMGTPmtknO/v7++Pv7c/z4cTp16sSYMWOYNWsWJpMJo9FI165dLfm7vr6+hIaGMnr0aORyOXK5nODgYBQKRZntTpw40XITrl+/PgEBAUilUt5//30mT56MyWRCo9Ewc+ZMvL29mTdvHu+++y4mk4n33nvPMo3m5ubG2rVr+eabb1AoFIwcObLUfqZNm8bixYsRBAGZTMb06dOrdI4bNWrEihUrSuUtg3nKbt68eezduxetVsuIESNwdHRk0KBBlvG5urrSo0ePKu2nb9++zJs3j2+//bbKovBu8fDwYM6cOUyfPp3g4GDeffddtFotr7/+OgqFgg8//JD//e9/2NnZlZuXN2rUKGbNmsX3339v+Zuq6JolJyeTlpbGe++9R25uLh988AEymYwmTZqwatWqMtPed8LkyZOZM2cOJpOJ9u3bW4yri3PXFAoFCQkJFnEOZoEbEBDAxIkTUSqV2NjYMGPGDDQaDRcuXGDMmDGYTCZefPHFMte8KkiEkjL9PnLo0CGOHDnC/PnziYqKYvny5axZswYwz7u/++67bNu2zZJ4X79+fXwqeTo0GAyPlfCqsP2DtRXDg3qjbPZ/HE+14lK2HAEJ1lKBtk4GXqgjo4U6k5YOBSilELFHxe7vVJw4Z67wWTAl87GcSnwQ18yo1f7bCuLSJeQ2NtQZMIB6w4Zh16hRpesWVyhqzq02eyg6N0LbZlxRhWLZG0NJHofv451gs2QJhjZtMDz33BN3bMXcL+F16dIlyxSQiIhI+RS3vqhqkcHjQEpKikXk3coDi3i98MIL/PLLLwwaNAhBEAgKCmLfvn3odDp8fHzw8fHB19cXhUJB3bp1LeHoJ4FbI1t6tZqb9RuhecUdnbML6yUSrOIF2jga+KBhLp2d9bR0KMBKVnxDMOdhROxRMWVBcZRLL+ZvVUD2n38SFx7OtZ07MebkYNekCS2Cg6nz+uvIK8kdAXOFouZ8GOoL4Uj1WejdOpHVYwF69+5PXoViJUhv3ECakYGxaVNyJ0582MMREREReWJ4YBGve83jEvEqKbpGf9aPxPqN+CbZGpMA7ZwK6Oyip7OzgdaOBqzLyefefbgaEZHmhNfHPcpVknt9zUwGAzcOHiRuwwbSTp40t4Lo2xdPPz8c27S5bQ6ELCOmqEJxu7lC0auP2UPRtfUdj+VR/j5WBdn16zgVJR3/c+wYlJj6edyPrSLEiJeIiMi95JGIeD2tbD+QAN3bU33gc6yWaXBMNTHaU8tb7jo8NIWVrmuOcMkBOR2DAFnpAAAgAElEQVRb6cUoVznorl8nPiKCq5s3o09NRe3uTtOPPqKuj0+lrSCKUSSfRfPbSqxjvi6qUHyzqELR8wGM/tFDdvUqTgMGIM3NJX3z5lKiS0RERETkvyMKr/tEdJacmYcNnH7DF6yU1HE08JF7Jq/Uyis3slWSJyWP634hmEzcPHqU2PXrSfnhBwBce/aknp8f1bt2RVLUkLHiDQhYxf9g9lBMPIHJyp7cdu+hazECk+bOyoKfJGSxsTgPHIgkP5+0rVsx3oUVhoiIiIhI5YjC6x6SXwgHklQsPC0hQW4PFMCpaN5raWRa34orUIqFVjHFgqtjKz1DX5PRv6cougD0aWlc3bKF+IgIdAkJWFWrRoPx4/EYMgT1Lb2FyqXQUFShGFJUoViLrOfmkNd08JPjofgfsPniCzAYSNu+HWOTJg97OCIiIiJPJKLwugck6GRsiFezJUFNRoEUUlPhx29oV5jMwJfrMtS3fDPlWyNbHVvpLf8WTymac08e2KE8cgiCQPrp08Rt2MCN/fsxGQw4d+xI0w8/pOZLLyFV3t4D0VyhuKmoQjGJAufGZPZaRl79fretUHyayJo3D1lyMoW3ePGJiIiIiNw7ROF1lxQKcOSmFeHxan64aYVUAr1q5BMf/j2/7zpT5KPYi4g9Kt4IUJW7jZKCS8zdKk1Bbi7Xd+0ibsMGsn//HbmtLR5Dh+IxbBh2JTphV4ZUexNNVFGFoiG7qEJxEXr3bk9VhWJlyKOjsQsKImPVKgR7e1F0PcFERESwbds2tm/fjpWVVSnfv2KKPQsBjh07xrZt2wBzh3FfX1+6d+9eapuBgYFcuXIFOzs7BEEgKyuLwYMHW7wgz5w5w/r16xEEgYKCArp3746Pjw8SiQSTycTGjRs5efKkxfOu2MuwJG+88QY1atRAKpVSWFhIXl4eU6dOpXHj8h9oq0JJn8N7wSeffEJCQgIfffTRXfV1qoiYmBhycnKqbL69du1ajh8/jkwm4/3336fJLZHr06dPExISgkwmo127dowePRowt3OIjIyksLCQLl264O/vz+eff87ff5tbIKWlpWFjY0NoaOg9O7anGVF43SFpeilbrqnYGK/mWp6cGlaFTGiQi+q3CxxZd4nYv+tg12AUu086s/skZaJZJREFV1my//jj31YQubnYe3vTcuFC3Pr3R66uWgd+WUYMNmdXobq8HQoLyPd6uahCsdV9Hv3jhSIqCqfBgzHZ2CDNyqJQ9EZ9ovn222/p0aMHhw8fvq1JdnR0NFu3bmXhwoWo1WqysrIYPXo0Hh4eFpuZYootg8BsiTN06FD69OlDXFwcy5cvZ+HChbi4uGA0Glm0aBGbN29myJAhbNq0iaysLFasWIFUKuXy5ctMmzaNLVu2lGnIuWTJEqyszL+lv/76K2vXrmXhwoX38Oz8N3799Vf2799/z7d79OhRnJycqiS8/vzzT86dO0doaCgpKSnMmDGDsLCwUsusWLGC2bNn4+Hhwbhx44iJicHKyorIyEiWL1+OQqFgzZo1GI1GJkyYAIDRaGTs2LFMmzbtnh/f04oovKqAIMCZDAXh8Wr2JakwmCR0dtbTNfUyf4WfZI+2IbEpdYHaYONBfgFA2WlDkfIp1Ou5ceAA8Rs2kHbqFFIrK2r360c9Pz8cW7Wqsh2GIvksNr+twCrmG3OFYpNB5gpFBzGKcyuK06dxGjoUk6Mj6Tt2UFiVHDmRx5azZ89Su3ZtXnvtNebOnXtb4bV3717efPNN1EUPO/b29oSGhmJra1vpemlpaSiVSiQSCbt372bYsGG4uLgAZlum8ePH4+/vz5AhQ9i7dy9hYWFIi4phGjduzJo1a8rtgl6S5ORkyziOHDnCzp07LZ8FBgYSGxvLpk2bkMvlJCUl0aNHD/z8/IiPjycoKAiVSoW1tbVlG4cOHbI073Zzc2Pq1KkcOnSIX375Bb1eT1paGgMHDuTnn38mNjaWgIAAi80SwKJFi8jJyWHq1Kl8+umnBAUFkZiYiMlkwsfHh549exIQEICDgwM5OTksXLiQzz77jGvXriEIAqNGjaJ169Z8+eWXnDlzBkEQ6NmzJ88//zwHDx5EoVDQsGFD1q1bR17ev/cRDw+PUubUFy5coH379kgkElxdXSksLLRY+hTToEEDsrOzMRqN6PV6pFIpv/32G40aNSIwMJDU1FT8/PxKXYMdO3bQrl27MpFIkbtHFF6VoDNK2J1ozfp4DZeyFdjKTQx11zHMXcepPdHm/ly2rcHlOVCBZ60MatQQhVZV0V67RvzGjVzdsgVDWhoaDw+azpqF+5tvonRyqtpGBBP/ViiexGTlQG7799E193+qKxQrQ3HqFE6+vphcXUnbtg3Tf7DjEKk6W69asfmq9T3dpq97Pj7uZaPpt7Jv3z769u2Lu7s7SqWSS5culbtc8UNOampqGZuWivxzV65cSXh4OCkpKXh4ePDJJ58AcOPGDfr27VtqWY1GQ35+PiaTifz8/DLbtK8g6jpx4kQMBgOpqal06NDB4juZkJDAokWLsLa2ZsGCBfz6669Uq1aN5ORkwsPDKSgo4NVXX8XPz4/Q0FBGjhxJ+/btiYiIID4+nqysLMLCwli3bh0ajYalS5cSGRmJSqVCp9Px+eefc/jwYbZu3crq1as5e/Ys27dvLyW8Jk2axI8//khwcDA7duzA3t6eWbNmWSyC2rZtC5ibiHft2pXdu3djb2/P9OnTycrKYty4cWzatIlvvvmGFStW4OLiwsGDB6lWrRp9+vTBycmJJk2a3DbCp9VqS50/tVqNVqstJbw8PT2ZMmUKdnZ2eHl54e7uzrFjx4iKimLVqlUYDAbeeecd1qxZg62tLQUFBURGRlpcZkTuDaLwKoe/cmSEX9Ww/ZqKHKOUJnYFLGieif6n86z7QsKOPC+ysz3B1RNUHkBxy4d8IP+hjv1RRygsJOXIEc5s2cK1b74BiYSaL75IvWHDqPbcc7dvBVFMoQHVn5FozoagSPsTo21tsp6bW1Sh+KRZON9bCmvVwvDMM2R99hkmsbnnE092djYnTpwgIyODHTt2kJuby86dO1GpVBQUFJRatrDQ3FvQ1dWVmzdvljJvvnDhAk5OTrjdEh0tnmo8fvw4ISEh1K5dG4Bq1aqRlJREgxI5mVqtFoVCgVQqtRgta0q4Sfz444+0bdu21Hvw71TjqlWrSEpKsogJR0dHAgMDUalUXL161dKw0tPT0+L/WDxFGRcXZ8l5atasGfHx8dy4cYN69epZ9teyZUtOnTpFkyZNLOO2sbHB3d0diUSCra0tBoOhwnN99epVi9DSaDR4eHiQmJgImE2jwZy3df78eX7//XfLOc/KymLOnDmsWrWK9PT0Unl3xUyePLnSiJdGoyll2KzT6bCx+bdaOycnh40bNxIREUG1atVYsWIFW7Zswc7OjlatWqHRaCxjvnbtGk2aNOH06dO0bNmy1HZE/jui8CqiwASHkq0Jj1fzS5oVSqnAKzXz8fPQ8sfBC6yaLyc2xd0itOzsbuBSTSVGuKqIPjWVq1u2ELdxI3nXr6NydaXh++/jPmQI6qIf6qog0eegvrQJzblQc4WiSxMyei0nv35fsULxNsgvXsTYpAkmNzcyIiIe9nCeOnzc9VWKTt1rDh06xCuvvGKJEuXn5zNgwAAGDx7M0aNHLdGbqKgoPDw8AHj55ZcJCQmhdevWqFQqMjIyCAoKIjAwsML9dOrUiYsXL7JgwQICAwPp378/wcHBeHt74+zsjNFoZOnSpRY7uN69e7N27VoCAgKQSCRER0ezbNkytmzZUuE+Ro8ezfjx49m1axe9evUiLCyMXbt2AVhykoBy0xPc3d25ePEizzzzDJcvXwbMLgXx8fHk5eWhUqk4d+6cxXy6qikOt+7j/PnzdO3aFa1WS2xsrCVyWDyl6u7uTrVq1fDz80Ov1xMeHo5KpeKHH35gzpw5CILA0KFD6dmzJxKJhGJzmdtFvJo1a8bKlSsZPHgwN2/eRBAEHBwcLJ9bWVmhVqtRqczFXs7OzmRmZvLMM8+wa9cu9Ho9JpOJ+Ph4i7j+7bffyhWBIv+Np154JeVJ2ZSgZtNVNSl6GW4qIx82zkb+63m+W3uZ+cCJizXBpa9lOvGdoRKGvirBHN0SI1wVIQgC6adOERceTuKBAwgFBbh07oz3rFl4+/qSkZ1d5W1JtSlFFYobiioUO5PZ8zMMdbuKFYpVwOrbb3EcPZqc//0P7XvvPezhiDxA9u/fz8yZMy2vra2t6datG3q9HrVajZ+fH2q1GoVCwZQpUwDw9vamX79+TJgwAblcjl6vZ8yYMXh5eVW6L39/f/z9/Tl+/DidOnVizJgxzJo1C5PJhNFopGvXrvj6+gLg6+tLaGgoo0ePtkSngoODUVTiliCVSpk+fTrjxo3jueeeo3nz5owYMcKSs5Wamlqh5dMHH3zArFmz2Lx5Mw4ODiiVShwcHHj77bcZP348EokENzc3xo4dy+HDh+/0NAPw6quvMn/+fMaOHYter8ff37/UVF/xMsHBwbz77rtotVpef/11lEoldnZ2DB8+HFtbW9q3b0+NGjVo1KgRK1aswN3dnTZt2lS670aNGtGiRQvGjBmDyWTif//7H2CuLD1//jwjRowgICCAiRMnolQqsbGxYcaMGdjZ2fHKK68wduxYBEFg+PDhlinghIQEXnrppbs6FyIV89R6NUZnyfniLxuLb+Lz1fX4eejoXl3Plk2lTa0vpb1CdkGth9JB/nH0xivIyeHazp3Eb9hA9h9/ILezo+6bb1LvrbewLZq6qOpxyTL+xubMKlR/7ACT0Vyh2HosBa5VK69+GDxq18z6wAEcxo6lwNub9M2bEUo8Bd8pj9qx3StEr0YREZF7iejVWAKtUcKiP20IjdVgrxAYU+Sb6F7CN3H3bnPvEnMvrsa8EeAE6MXpxNuQ9fvvxG3YwPWdOzFqtTg0b07LRYtwe+21KreCKEaRdAabMyuLKhSt0DUZjLb1aLFC8Q6xjozEYfx4Clq1Ij0iAqGCBGkRERERkQfDUyW8DqdYMT3ajsQ8OW+5a/mwcQ72CnPALyLiskVwXbqUhmeL7uw+2YHdJ+HSXwqa1i+obNNPLcWtIOLWryf9t9+QWlvj1q8f9YYPx7GKTf8sCCas4r43Vyje+PXfCsUWIzCpXe7PATzBSNPSsJ80CUO7dmRs2IAgJsiKiIiIPHSeCuGVki9l1kU79iWpaGBTQGTnVNo7/SukIiJKTy261OtMbPZzxJ4z9+FqWr+A/i+I0a6SaK9eNbeC+OorDOnpaDw98f74Y+oOHIjylpyG21JoQPXnbrOHYvoVc4Vi17nkNRErFP8LJmdn0rduxdi4McIdRhxFRERERO4Pdyy8jEbjbRvcPSqYBIi4qibosi16k4SpDXMY65WL8paOBSWnFrFtzZQF5hyYh5HT9SgjFBaS/P33xG/YQMqRI0ikUlx79TK3gnj22aq3gihCos9BfTECTdQasULxHqIOD0dQKMjz9aXgNgm5IiIiIiIPliorqMjISFatWsX169f5+uuvWbNmDdWrV+fdd9+9n+O7a65qZbx3zoHTGUqeddEzv1kWnjaFZZaLiLjMiRNJdOxYUxRdFZD/zz9c3bKF+I0byUtMxNrVlYYTJ+IxZAiqu0hElmpTkJ1ZTPVTXyI15KB3e1asULxHqENDsZ89m/xevcgbPFg8nyIiIiKPGFUSXpGRkQQFBTFixAhCQkIAc+lqcHAwSqWSUaNG3ddB3infJFsx4ZwDEgksbZnJALe8MvefiIjLrNokJzbF3Ag1RWoviq4SCIJA2smTxIWHc+PrrxEKCqj27LM0mzMH1xdeQFpJyXdFmCsUQ1D9sfPfCsU24yio0eI+HMHTh2b5cuyCgsh7+WUyV6wQRZeIiIjII0iVhNfatWuZOXMmffv25csvvwRg8ODB2NjY8MUXXzwywksQYN4ftiz/24bm9gZWt82krrp0lKs4if7W3lw1aqjFZqhAQXY213bsIG7DBnKuXEFhb4+nvz/13noLm7v06lIk/VZUoXjIXKHYdDCK56eSKdx9WwOR0tgsWYLtwoXkvfoqmcuWwWOSDiDy4IiIiGDbtm1s374dKysrAgMD6dmzZ6kGmX379mXfvn0AHDt2jG3btgGg1+vx9fWle/fupbYZGBjIlStXsLOzQxAEsrKyGDx4sMUL8syZM6xfvx5BECgoKKB79+74+PggkUgwmUxs3LiRkydPIpPJALM1UElPwLy8PEaOHMmkSZNo1cpscj937lxatmxJv379SExMZOXKldy8eRNra2usrKwYN24cnp6ehIWF8d133+Hi4kJhYSEODg589NFHZbri3w3Jycn8/fffPPvss1Vafu/evURGRiKTyRg+fDidO3cu9fmVK1dYuHAhcrmcOnXqMG3aNKRSKSdOnGDt2rUANGzYkA8++ACtVsvcuXPRarUUFBTw3nvv4e3t/Z+PSeTBUaVf56tXr5brjt6yZUtSUlLu+aDuBkGA2ZfsWBOnYUhdHZ94Z2EtK7vc7t1/c+7vOuDSGxCtforJvHiR+A0buLZrF4U6HQ4tW9Jq8WJq9+t3x60ggKIKxcPYnFmJ8sYpTNaO5LafUFSh6IyzkzM8gf2gHhaCXI5u4ECyFi8GWTlffJGnnm+//ZYePXpw+PDh25pkR0dHs3XrVhYuXIharSYrK4vRo0fj4eFBvXqlW7oUWwaB2Z5o6NCh9OnTh7i4OJYvX87ChQtxcXHBaDSyaNEiNm/ezJAhQ9i0aRNZWVmsWLECqVTK5cuXmTZtGlu2bLHkEatUKmbPns2MGTMsQgqgX79+5OfnM3XqVKZNm2YRHr///juLFy9m+fLlAPj4+Fg65a9atYo9e/ZYGrj+F86cOUNCQkKVhFdaWhrbt28nLCwMg8HA2LFjadeuHUql0rLMunXr8Pf3p1OnTnz88cccP36cVq1asWLFCpYvX46DgwObNm0iMzOTnTt30qZNG3x8fLh69Soff/wx69at+8/HJPLgqJLwqlmzJn/88YfFSqGYEydO3NNmg/+FH/9RsiZOw8h6WuY0zS41yxKxR8WqCIHUf/LQ6npRaOMOiFOKhfn5JO7fT1x4OBlnziCztqb2a69Rz88PxxZ3Of1n1JsrFM+GoEj/C6OtG1ldPzF7KCrEyrp7iiAgTUzE5OaGdvx489OHOL0oUg5nz56ldu3avPbaa8ydO/e2wmvv3r28+eabqIseuuzt7QkNDcXW1rbS9dLS0lAqlUgkEnbv3s2wYcNwcTG3gpHL5YwfPx5/f3+GDBnC3r17CQsLs1jpNG7cmDVr1pQp3mrQoAEDBgxg5syZ5OTksHLlSgB+/vln2rRpUyra06RJE5YtW1bu2HJycmjYsCFgtlHatm0bSqUSNzc3pk6dCkBQUBCJiYmYTCZ8fHzo2bMnu3bt4uuvv0YikdC8eXPGjh1LREQEer0eb29vfv75Z4sfI4CtrS3z5s2zvP79999p1qwZSqXSsr+YmBgaN25sWaZ+/frk5OQgCAI6nQ65XM7Fixf5v//7P5YtW2YxHHd0dMTHx8ci2goLC0sJOJHHgyoJrxEjRvDxxx/zzz//IAgCp06dYteuXaxfv95iS/CwOZ5mhVwiML1xWdFVnLtFXhZ2dkpcqhXb/jydoksbH0/chg0kbN2KISMDm//7P5rNnUudAQNQ3mVXc4k+21yheG4NMm2yuULxpRXmCkWpOO11zxEE7GbPRrV9O6nffUehm5souh5xth6wYvM+63u6Td+++fi8fHv/x3379tG3b1/c3d1RKpVcunSp3OWK/QlTU1MtHoPF2FXQfHflypWEh4eTkpKCh4cHn3zyCYBFLJREo9GQn5+PyWQiPz+/zDbt7e3L3UefPn0IDQ3lrbfewtrafA6TkpJKGXZPnToVrVZLamoqX3zxBQBbt27l+++/Jzs7m7y8PIYPH05WVhZhYWGsW7cOjUbD0qVLiYyMtOx/1qxZaLVaRowYQdu2bTlw4AATJ07E29ub3bt3W7wUExIS6NKli8XrsiJuNatWq9Xk5uaWWqZOnTp89tlnrF+/HhsbG1q1asXRo0c5e/Ys69evR6VSMW7cOLy9vS1m22lpacydO5f333+/0v2LPHpU6Y745ptvYjQa+fLLL8nPz2fGjBnUqFGDqVOnMmjQoPs9xipxJkOBt30BqhKzLAEfZrHrx6KIXOo+FszUMHRoY57GaUWT0UjK4cPEbdjAzaNHkchk1Ozdm3rDhuHSufNdGcICSHOT0UStQR290VyhWOdZMl9YLFYo3k9MJuxmzEATHk7uqFEU3oHJuMjTR3Z2NidOnCAjI4MdO3aQm5vLzp07UalUFBSUbgxdWGjOiXV1deXmzZvUL7L4Arhw4QJOTk6lxA78O9V4/PhxQkJCqF30faxWrRpJSUk0aNDAsqxWq0WhUCCVSrG1tUWr1ZbKufrxxx9p27ZtmTysefPm4e/vT2RkJJ07d8bLy4vq1avzxx9/WJYJDg4GYNSoUZbjKDnVuG/fPgIDA3nnnXeoV6+eZR8tW7bk1KlTSKVS2rZtC5gFooeHB4mJicyYMYPNmzcTEhJSbi7VvHnzKo14qdVqdDqd5fWtQgzg888/Z+XKlXh6erJz506WL19O586dady4Mc7OzpZx/vXXX9StW5eYmBhmzZpFQECAJfdN5PGhSsLrxo0bDBo0CF9fX9LT0y0Gm4WFhVy8ePGhJ/b9lQ2n05WM8tRa3ovYo7KILk+7Y7wztlh0PV3k37zJ1c2bza0gkpKwrlmTRpMm4e7ri8rV9a63K0v/C5uzq/6tUKz/Crmtx2Gs0fwejl6kDIWF2E+ZgnrLFnLHjSNnxgxR4D4m+Lysr1J06l5z6NAhXnnlFQICAgDIz89nwIABDB48mKNHj1oiNlFRUXh4eADw8ssvExISQuvWrVGpVGRkZBAUFERgYGCF++nUqRMXL15kwYIFBAYG0r9/f4KDg/H29sbZ2Rmj0cjSpUstQqh3796sXbuWgIAAJBIJ0dHRLFu2jC1btpTa7ldffYVMJmPIkCF4eXkxe/ZswsLC6NKlCxEREaXuQdevX+eff/4p90GyRo0aFBQUULNmTeLj48nLy0OlUnHu3Dnq1KmDXC7n/PnzdO3aFa1WS2xsLLVq1SI8PJzJkydjZWXFxIkTiY6ORiqVYjKZAJg+fXql579JkyasXr0avV5PQUEB8fHxeHp6llrGzs7OIgRdXFyIjo6mYcOGxMbGkpmZiY2NDZcuXaJfv37ExcXx0UcfMXfu3FLCWOTxoUrCq0ePHvzyyy84OTnh5ORkeT8pKYkhQ4Zw/vz5+zbAqrDhLxkCMKZIeJWcXvS0O8bPXz9dX05BEEg9cYK48HCSvv4awWik2nPP0Sww0NwK4j9UvClunMbmzEqsYw8hyK3RNfVF23oMhfbu9/AIRCpCvWED6i1byJkwgdzJk0XRJXJb9u/fz8yZMy2vra2t6datG3q9HrVajZ+fH2q1GoVCwZQpUwDw9vamX79+TJgwAblcjl6vZ8yYMXh5eVW6L39/f/z9/Tl+/DidOnVizJgxzJo1C5PJhNFopGvXrpbkdl9fX0JDQxk9ejRyuRy5XE5wcDCKEq1qLl68SGRkJGvWrAGgQ4cOdOzYkcWLF/Phhx+yYMECQkJCCAkJobCwEJlMxpQpU3AteqgsnmqUyWTk5+czYcIEHBwcePvttxk/fjwSiQQ3NzfGjh2LVCpl/vz5jB07Fr1ej7+/P46Ojnh6ejJy5EgcHByoVq0aTZo0QaPREB4eTsOGDenZs2el58TZ2ZmBAwcybtw4BEFg9OjRWFlZERcXx86dO5k0aRLTpk1j9uzZyGQy5HI506ZNw9HRkXfeeceSzvP888/j6enJ1KlTMRgMLF26FDBH54qjfSKPBxJBEITyPti5cyd79uwB4NSpU7Rq1arUHwSY3bcLCws5fPjw/R/pLRgMBtKKquIG/FoDQ4GRvc+aX78R4MSJc1aQuo+O3kns3Nm3sk090jg7O1uO83YYsrK4tn078Rs3kvPXXygcHHD38cHjrbewueUJ644QTFjFfYfNbytRJp3GZO2ItoU/uub+mNTOd7XJOzmux437emwGA9YHD5L/2mv3Z/u34Um9biWP614WDF26dIkaNWrcs+2JiIg8HqSkpNC0adNyP6sw9NGzZ0+ioqIsyfS1a9e2JDWCOQmzSZMmvP766/d+xHfI1VwJzzobS71np7hBds5Z+vevPPHxSSDzwgXiNmzg+u7dFObl4di6Na0//5zaffsiU6nufsNGPao/d2FzJgR5xt8Y7eqQ1S2QvCaDxArFB4nBgG1wMLnjxiE4Oz800SUiIiIi8t+pUHjZ29tbqlNcXV0ZMWKEpbT4UUIQIE0PjkqT5b2UFB3Z2QY6dqz5xOZ1Feblkbhvn7kVxLlzyFQq3Pr3p96wYTg0/295VhJ9NurojWYPRW0KBdWaihWKDwu9HsdRo7A+fJiCpk3JfwQedERERERE7p4q3UUDAgJIT0/n8uXLloRCQRAwGAxER0czduzY+zrIytCbIL9QgqPCPK6IPSpibzgAWfTvX3k+wuNIbmwscRs3krB1KwWZmdh4eZlbQQwciLKCUuyqYq5QDC2qUMxFX6cLmS98jqHuc2Iu0cMgLw/Ht9/G+uhRsubPF0WXiIiIyBNAlb0aZ82ahcFgQCKRIAiCpWqkbt26D1V4GQXzOBTmHnysijCnrHnWSHhiol0mo5Hk774jLjycf44dQyKXU6t3bzz8/HDp2PGuW0EUI0//C02xh6JQSH79vuS2GYuxulih+LCQ6HQ4Dh+O8pdfyPzsM7PhtchjScnfSxERkSefClLnLVRJeK1atYrXXnuNUaNGMWDAANatW0daWhqzZ89mzJgx92Sgd0tB0QyjXCIQEXGZ2NxCg0kAACAASURBVBhPIIt3xhorXe9xIC85mXOrVvF7aCj5SUmoatWi8ZQpuA8ejPU9SNhV3DhVVKH4rblCsdlQtK3GUGhf9x6MXuS/IMnNRZaURNbSpeQNGPCwhyNyl1hbW1t6VYniS0TkyUcQBLRabamc+FupkvC6fv06ISEh1KlTh0aNGnHz5k26devGjBkzWLZs2UNNsC8sinid/S2ZyE+04OKBZ62MxzbaJQgCqb/8Ym4F8c03CIWFVO/WjRaffkqNnj3/UysI8w5MWMV+a/ZQTPoNk7UjOR0+QNtiOP/f3r3HyVwvfhx/zczed9krDsWWS0pyS0koQuVSbHJnOSnJ6VTihPqREEpUVuSWXJJbjhASdU6R6pDriWhDKLe9YK+zO/P9/bFrj41ds2tnZmf2/Xw8OpmZNfP+2HPs+3y+38/nYwQWb4WilBxTSgpGQAD2ihU5u2UL6DgQj1atWjV+++03zpw54+4oIuIiAQEBeScMXI1DP8UDAwPzztOKjo7m0KFDtGzZkttuu41jx46VTNJisubOeO398RQE3wHAoD6e9/8srcnJ/LZiBUcXLiQlPh7f8HBqPPUUDf/+d7LCw6//A7IzCTz4CSE/zsQnKT53heLrpNXpDlqhWCqYkpOJ6NWL7Nq1Of/22ypdXsDX15caNWq4O4aIlCIOFa+GDRsyb948XnnlFerUqcOnn37KwIED2bNnzxVHO7halj2nZJntdsqX9+P2upkedQZj0p49HFmwgJOrV2PLyCDizjtpNG0aN3TsiCUggPLXuW9SzgrFhQTvnpe7QrEuSQ/PIKNWR61QLEVMCQlE9uiBz+HDpLzwgrvjiIiIkzj0k/fFF19kwIABVKtWjR49ejBr1iyaNGlCamoqsbGxzs5YqEszXhf++AsXsqoArj+So6iy09I4uWYNRxYuJHn3bixBQVR9/HFuio0lrISOXzKn/HHZGYopZFa7j+QH38VatYVWKJYy5nPniOjWDZ+jR0maP5/MVq3cHUlERJzEoeJ16623snnzZtLT0wkJCWH58uVs2rSJiIgI2rVr5+yMhbLmznidOZZzf1JM29I725USH/+/rSDOn6fcLbdQb/x4qj7+OL7ly5fIZ/gkHCL4x5kEHlyVu0Lx0dwVineUyPtLCTMMwmNj8Tl6lMQFC7C28P4Nf0VEyjKHrzUFBgYSmLsLeoUKFejduzcAixcvpk+fPs5J54CM3OKFYeTcVN8pw21ZrsaelcUfmzZxdMECzm7disnXlyrt2nFz//5ENmlSMiudDON/KxSPfJG7QrEvqQ0HaoViaWcycfH//g/MZqz33OPuNCIi4mQFFi/DMJg3bx7r16/H19eXRx99NK9sARw+fJhRo0axZ88etxavTFtOcQkK9KFSpSCgdBSv9D/+4OhHH3FsyRIyTp0i8IYbuG3EiJytICpUKJkPMez4//p57grFndgCI7h4zzBS6/XTCsVSznLiBH7ffkt6t25Y773X3XFERMRFCixe77zzDrNmzeKee+7Bz8+PiRMnAtC7d2/mzJnDtGnTCA4OznveXbIMYDekpUbi7vu7DLuds1u3cmThQk59/jmG3U6lVq2oP2kSf2ndGpPFUjIflJ1J4MGVhPz4fu4KxWpaoehBLEePEtG1K+bUVDLatMGIiHB3JBERcZECi9dnn33GkCFD8jZI/fTTT5k1axanT59m9uzZdOzYkVdeeYXwktjq4DrY7Cb4b86v3XV/lzUpid+WL+fIokWk/vorfhER1Hz6aW7q25fg6OgS+xxT5nmC9uauUEw7Q1bFO0hqN5OMmh20QtFDWH75hcju3TFlZJCwbJlKl4hIGVPgT+szZ87w0EMP5T1u3749I0eOZOnSpbz77rv5XnOnBGvO/mLBQWfp08m1u9Un7d7NkQ8/5MSaNdgzMoho3JhbX3yRKh06YPH3L7HPMV/8PWeF4v7FuSsU7yf5zjisVZtrhaIH8Tl0iIiuXcEwSFi5kuzbPHOTXxERKb4Ci5fVaqVcuXJ5j319ffH39+ell14qNaUL4IvP/eE4EFj42UglJTstjROrV3N04UKS9+7FJziYat26cXNsLKF16pToZ/kk/Izl6/lU3PMxGHYybsldoVihZLacENfy++47MJtJXL6c7Fq13B1HRETcoMjXp+666y5n5Ci2fdt9AYgKOAxUd9rnXDx8OGcriOXLyb5wgfK33kq9CROo2qULvpcV1OuWt0LxPQKObMbwDSKtXmzOCsXyVUvuc8R1MjPB35+02FjSO3XCCA11dyIREXGTQovX1bY6uHR0UGlhN4Cq8BfbAUq6eNmzsvjj8885smAB57Ztw+Tryw0dOnBzv35E3H13yR56a9jxj89doXjq0grFf+DfcggXSu/WZHINvj/+SPjAgSTNnk1Wo0YqXSIiZVyhxWvixIn5TtjOyspi6tSphISE5Pu6cePGOSedAy5dYDTZ7SX2num//87RxYs59vHHZJw+TVDVqtQZOZLonj3xj4oqsc8BIDsj5wzFnTPxSf6V7NBozrecQFqdbuAbhH9QJKQX/8ggcR/f778nom9f7JGR2CtWdHccEREpBQosXnfddRenTp3K91zDhg05d+4c586dy3vO0Vkfu93OmDFj+Pnnn/Hz82P8+PFEX7bib+/evUyaNAnDMKhQoQKTJ0/Gvwg3qF/v3JNht3P26685snAhf2zaBIZBpdataTB5MpVatSq5rSBy/XmForViPZLavU9GzfZaoegF/L79lvDYWOx/+QsJK1Zgr1zZ3ZFERKQUKPAn/KJFi0r0gzZv3ozVamXZsmXs3r2bSZMmMXPmTCBns9ZRo0Yxbdo0oqOjWbFiBSdPnqR69WtfOjQu+8/isCYmcmzZMo4uXkzqkSP4RUZSa/BgburTh+BqJb/re84KxTkE7VuMOSuVjOiWJN85HeuNzbRC0UuY9uwhok8fsqtVI3H5cs12iYhIHpdNrezcuZMWuefQNWjQgP379+e9duTIEcLCwliwYAGHDh3i/vvvd6h0ARhG0cuKYRgk/fgjRxYu5OSaNdgzM4ls0oTbhg2jcvv2JboVxCU+5w4S/OP7BP68Cgwjd4XiYLIr3F7inyXuZdSpQ+qAAaQOGoQ9UicIiIjI/7iseKWkpOS7N8xisZCdnY2Pjw9JSUns2rWLUaNGER0dzaBBg6hbty5NmzYt8P0sFguRkZE5N/sbOdtdRF7jh1xWairxS5dycPZsEnbvxjckhNr9+3PrwIFE1HXCFg2GgenYVixbp2A+tAHDNwj73U9ja/oclvCbcOQ2ax8fn2uOyxN547hMmzZh1KuHT2AgTJ2Kn7sDOYE3ft/Ae8clIqWPy4pXSEgIqampeY/tdjs+PjkfHxYWRnR0NDVr1gSgRYsW7N+/v9DiZbPZSEhI4GJKOBh+ZGVnkZBw9ZvQLxw6xNGFC/ltxQqyL16kfJ061J80iRsfewzfkBAMKPD3FovdRsCvnxO8cwa+p37MW6GYc4ZiBNgBBz8vMjKyZLOVEt42roB16wgbPJj0mBhYvNirxnY5b/u+XXL5uCrrfjwRcSKXFa9GjRrx1Vdf0b59e3bv3s0tt9yS91rVqlVJTU3l2LFjREdHs2PHDh5//HGH3jc9PRsC/IiJqZnvebvVyh8bN/LrggUkbN+O2c+PKh075mwF0bhxyW4FcUl2BoEHcs9QvLRCsdVE0m7rqjMUvVjAqlWEPf88WY0acWH8eHQIkIiIFKRIxevcuXPEx8dTv359UlNTizQ137ZtW7Zt20aPHj0wDIMJEyawdu1a0tLS6N69O6+//jpDhw7FMAwaNmxIy5YtHXpfAxOYoE+fnONX0k6c4OhHH3FsyRIyz54lqFo1bn/lFar16IG/ky4lmDKSCdq3iODdc7Gknc1Zodh+Fhk12oO5ZFdDSukSuHw5oUOGYG3alKQFCzCCg90dSURESjGTYRjXXBJotVoZM2YMq1atwmw28/nnnzNp0iRSUlKYPn16vqOFXMVqtZKQkEB0p/Jk+wfw4zPLOLJgAac2bwbgL61bc3O/flRs2RKTkzZ9NV88SfCu3DMUc1copt45uERXKJaFSzsey2ol6uGHsVeoQOL8+RCUM6vpFWMrgLeOTZcaRcRVHJrxmj59Ovv27WPJkiUMGDAAgCeffJIRI0YwefJkxo4d69SQ12IybGzv3Rv/qChuefZZburTh6Abb3Ta5+WsUJxJ4M//zF2h2Cn3DEWtUCwzDAP8/HK2iwgJgcs2GhYRESmIQ8Vrw4YNjB8/nkaNGuU917BhQ8aNG8eLL75YCoqXQaU2bWgydy5mPyetJTMM/E5+R/DOGQQc3YLdJ5C0ev1zz1B0XsmT0id49mx8d+wgecYM7CV9koGIiHg1h4rXmTNnqFKlyhXPR0VFcfHixRIPVTQ5l/T8o6KcU7rsNgLiNxK8cwZ+p3dhC4zkYtOXSL0jNmeFopQpwdOnU37CBNI7dsyZ9RIRESkCh4rXbbfdxpYtW+jfv3++55cvX86tt97qjFxFVuL3cV2xQvEmzreaRFqdruATWLKfJR4h5O23KTd5MukxMSS/+y746GgnEREpGod+cgwbNownn3yS3bt3k52dzZw5c4iPj2fPnj3Mnj3b2RmvyYRRYjezmzKSc89QnIsl/RzWivVJaj+bjBrttEKxDAt5913KTZ5MWrdunJ8yBUr47E4RESkbHCpejRs35uOPP+aDDz4gOjqaffv2UbNmTV599dV8+3G5g2Ey5ewQf50zXuYLJwjefWmFYhoZ0a1IvnMw1hvv1RmKQmazZpiffJILY8aAk1bJioiI93OoeG3fvp2mTZsyefJkZ+cpFpNhL3Y58jl3gOCdMwk8tBoMg/TanUlt9AzZFeqUcErxOIaB39atWFu0IKtxY7IaN3Z3IhER8XAOFa8nn3ySihUr8uijj9K5c2duvvlmZ+dynMmEyTCKthO9YeB3cjvBO2YQcOxL7L5BpNb7K2kNn9IKRclht1N+5EiCFy0iYdUqrPfc4+5EIiLiBRwqXv/+979Zt24d69atY9asWdSrV4/OnTvToUMHQkMdOerZBRy5/GO3ERC/IXeF4u7cFYrDSa0XixEQ7vyM4hlsNkKHDSNo2TJSnn0Wa5Mm7k4kIiJewqHiFRUVRf/+/enfvz9Hjhzhs88+46OPPmLixIm0atWKadOmOTtngXLu8aLwGa/sdIIOrCR45/v4nD9CdujNnH/gDdJue1wrFCW/7GxChwwh6JNPuPjii6QMHap7/EREpMQUeT38TTfdxJ133sm5c+c4deoUe/fudUYuhxkmE3azz1VnvEwZSQTvXUjQ7nk5KxQrNSCp2RwyajysFYpyVX5btxL0ySdcGDGC1Oeec3ccERHxMg4Xrz179rBu3To2bNhAamoqrVu35t1336VZs2bOzHdNhtmM2WbNN+NlvnCC4F1zCPrvR7krFB8gufFgrDc01eyFFMrasiVnP/+c7DvucHcUERHxQg4Vr9atW/P777/TqFEjnn/+edq1a0dISIizsznEbLNhN1nAbMbn7E+5ZyiuBpOJ9Fs6k9pokFYoSuEyMgh7/nnS+vfH2rSpSpeIiDiNQ8Wrc+fOdO7cmapVqzo7T7H4ZmcS8Mt6KiyZlbNCscEAUhs8iV0rFOVa0tKIGDAA/3//m8z77oOmTd2dSEREvFiBxev06dNUqlQJgG7duuU9dzWXvs4dLGY72Aws6ee40HQEafViMQLC3JZHPIcpLY3wfv3w+/ZbkqdOJb1HD3dHEhERL1dg8WrZsiVbt24lMjKS+++//6qrBo3c/bMOHDjg1JCFMWGAARl1upJ6t26GFseY0tII790bv//8h/PTppHepYu7I4mISBlQYPFasGBB3h5dCxcudFmgorKbLJgBfPzcHUU8iOHvjy06muS//pWMRx91dxwRESkjCixed999d96vf/jhBwYMGEBgYP49r1JSUoiLi8v3ta5mwsDm4wc+vm7LIJ7DlJSEKSMDe+XKnH/nHXfHERGRMqbA4pWYmEhGRgYA7733Hq1atSI8PP/u7j/99BMff/wxI0eOdG7KQtjMPvhZ08Gs4iWFMyUkENmjB9jtnNu0CSzay01ERFyrwOL19ddfM2LEiLx7ux5//PGrfl3btm2dk8xBPnYrNrMvJkeODJIyy3z2LBHduuFz7BiJH3yg0iUiIm5RYPHq3Lkz1apVw26306dPH2bMmJHvXEaTyURwcDA1a9Z0SdCCmABLdqY2RpUCmU+dIrJbN8wnT5K4cCHW5s3dHUlERMqoQvfxatSoEQBbtmyhSpUqhZ+H6Gaa8ZKClB81CvMff5C4ZAlZOvBaRETcqMDiNWrUKEaMGEFwcDDvv/9+oW8ybty4Eg/mOCPnX6W4FIp7XZg0CcuJE2TVr+/uKCIiUsYVWLyOHj2KzWbL+3VB3D0LdunTNeMll7McOULwzJlcGD8ee2Qk9shId0cSEREpuHgtWrToqr8utTTjJbkshw8T2b07psxMUgcNwla9ursjiYiIAODwNNHJkydJSUkB4D//+Q9jx47l008/dVqwotKMlwD4HDxI5OOPg81GwiefqHSJiEip4lBb2bhxIw899BB79uzht99+Y+DAgfznP/9hzJgxfPjhh06OeA0m3eMlOXz++18iHn8czGYSVq4k+9Zb3R1JREQkH4eK14wZMxg8eDDNmjXj008/pVKlSqxZs4Y333yTjz/+2NkZC5V3j5eKl9hs2CtVypnpqlXL3WlERESuUOh2EpccOXKEzp07A/DNN9/QqlUrTCYTt99+O3/88YdTAzpMlxrLLPMff2CvXJnsevU498UX+u+CiIiUWg79hAoPD+fcuXOcO3eO/fv306xZMwAOHTpEVFSUUwM6TDNeZZLv999T4f77Cbp0kLtKl4iIlGIOzXh16NCBYcOGERAQQKVKlWjatCnr169n/PjxBR4l5CoGJkwYurm+DPLbto3w2FjsVaqQ4eajq0RERBzhUPH6xz/+QZUqVfjtt9/o1asXFouF5ORkevfuzTPPPOPsjNdg5NznpRmvMsXvX/8i4oknyK5WjcTly7FXrOjuSCIiItfkUPEym8307duXlJQUfv31Vw4cOMCjjz5KSEiIs/M5TDfXlx3m06dzSlf16iQuW6bNUUVExGM4VLxsNhsTJ05k6dKl2Gw2DMPAz8+Pbt268fLLL2N252W+S7tJ6FJjmWGvVInk6dPJbNoUIzzc3XFEREQc5lDxmjlzJmvXruWVV17hrrvuwmazsWPHDuLi4oiKimLQoEHOznltmvHyegFr12IvVw5ry5ZktG/v7jgiIiJF5lDx+uSTTxgzZgzt2rXLe6527dpEREQwZcqUUlG8NOPl3QJWrSLsueewtmhB4v33q2iLiIhHcqitJCUlUadOnSuer1OnDqdPny7xUEWT+wNYP4i9VuCyZYT9/e9YmzYlae5cfa9FRMRjOVS8atSowZYtW654/osvvuCmm24q6UxFZ2jGy1sFLl5M2JAhOTNdCxZgBAe7O5KIiEixOXSpcfDgwTz33HMcOHCAhg0bArBz5042btzIG2+84dSADtMsiPcxDPx27SKjdWuS5syBgAB3JxIREbkuDhWv1q1b8/bbbzNnzhy++OIL/P39qVmzJrNmzaJ58+bOzugYFS+vYrp4EaNcOc6/+SbYbODn5+5IIiIi182h4gXw4IMP8uCDDzozy3XRPl7eI3jaNII++oiEtWtzNka1WNwdSUREpEQUWrzmzp3L+vXr8fPz4+GHH6Zfv36lt+DoHi/PZxiETJlCualTSX/sMewREe5OJCIiUqIKbCszZ85k6tSphIeHExoayuTJk3nzzTddma1IdHO9hzMMyk2aRLmpU0nr1o3kd98FH4cnZEVERDxCgW1l9erVvPrqq8ybN49Zs2YxYcIEVq5c6cpsRVNaZ+LEIUEffEBIXBypfftyfupUXV4UERGvVGDx+v3337nvvvvyHrdr146LFy9y9uxZlwQrKs14ebb0Ll24MGoUFyZN0mVjERHxWgX+hMvKysLvspVkfn5+BAYGkpGRUawPstvtjB49mu7du9O3b1+OHTt21a8bNWoUb731VrE+QzyM3U7Q3LmQkYERFkbqM89o5lJERLyay6YWNm/ejNVqZdmyZQwdOpRJkyZd8TVLly7l0KFDxXp/zXh5GJuN0BdfJHT0aALXrnV3GhEREZcosK2YTKYrVjBez4rGnTt30qJFCwAaNGjA/v37872+a9cu9uzZQ/fu3Yv3AZop8RzZ2VieeIKg5cu5OGwY6V27ujuRiIiISxS4bMwwjHz3eAFkZ2fnOyj7kj+XqKtJSUkhJCQk77HFYiE7OxsfHx/OnDnD9OnTmT59Ohs2bChK/jya8fIQWVmEPfsslrVruTByJKl//7u7E4mIiLhMgcVr4sSJJfpBISEhpKam5j222+345G4XsHHjRpKSkhg4cCBnz54lIyOD6tWr89hjjxX4fhaLhcjISCALgHLly+c+9i4+Pj7eNa5ffsH322+xT5lCwLPP4o2HAHnd9+wy3jo2bx2XiJQ+BRavmJiYEv2gRo0a8dVXX9G+fXt2797NLbfckvdabGwssbGxAKxatYpff/210NIFYLPZSEhIAMoDkJKamvvYu0RGRnrHuLKycvblCg/H9O9/E1GrlneM6yq85nt2Fd46tsvHVblyZTenERFv5rIdKtu2bcu2bdvo0aMHhmEwYcIE1q5dS1paWvHv67qc7vEqvdLSiHjiCayNG5MybBiGdqQXEZEyymXFy2w2M3bs2HzP1ahR44qvu9ZMV0FK7VFGZZwpNZXwfv3w276d9BKeRRUREfE0XnAmi5HzL91cX+qYLl4kok8ffHfuJDkujoxilmoRERFv4QXFK4dmvEoZuz2ndO3aRfLMmWQ88oi7E4mIiLidw9NE58+fZ/bs2YwYMYKEhAQ2btxIfHy8M7MVjWa8ShezmbTYWJJmzVLpEhERyeVQWzly5Ajt2rXjk08+Yd26daSlpbFp0yYef/xxfvzxR2dndIhmvEoHc0ICft98A+Scv5h5lX3fREREyiqHitfEiRN56KGH+Pzzz/H19QXgrbfe4uGHH2bKlClODegwzXi5nfnMGSK6dCF84EBM58+7O46IiEip41Bb2bNnD3369Mn/G81mBg4cyE8//eSUYEWlGS/3Mv/xB5GPPYbl+HGS5s7FCA11dyQREZFSx+Gb6zMzM694LiEhAT8/vxINVGwqXm5jPnGCyG7dMJ87R+KSJWQ1aeLuSCIiIqWSQzNeDzzwAO+8806+I3+OHz/OhAkTaNmypbOyFYnOanSfoGXLMCcmkrh0qUqXiIhIIRxqKyNHjuT8+fM0adKE9PR0unbtyoMPPoifnx/Dhw93dkbHaMbL9YycPdRShgzh3KZNZDVq5OZAIiIipZtDlxrLly/PsmXL+Pbbbzlw4AC+vr7UqlWLpk2bOjufwzTj5Vo+hw8T+vzzJM+Yge2mm7BVq+buSCIiIqVekTZQvffee7n33nudleX6aMbLZXwOHiSiWzcwmTBd5d4/ERERuTqHitftt99e6KrB/fv3l1ig4tKqRtfw2bePyB49MPz9SVi+HFvNmu6OJCIi4jEcKl7jxo3LV2yys7M5evQoq1ev5qWXXnJauCJR8XI6n59+IrJbN4zgYBJWrMB2883ujiQiIuJRHCpejxVwuPHtt9/OypUr6dSpU4mGKg7d4+V8tqpVybz/fi6+8gq2qlXdHUdERMTjXFdbqV+/Pjt37iypLNdHxctpfPbuxZSWhlGuHMnvv6/SJSIiUkzFbiuZmZksWbKEqKioksxTbLrHyzn8tm4lMiaGcmPGuDuKiIiIxyv2zfU2mw2TycQYd/9ANnL/rRmvEuf3r38R8cQTZN90Eyn/+Ie744iIiHg8h4rX+PHjr3jO19eX+vXrU7WUXHbSjFfJ8v/iC8KfeorsWrVIWLoUIzLS3ZFEREQ8nkPF6/vvv+fpp5/m5tK8ik3Fq+RkZBA6YgRZt91G4pIlGOHh7k4kIiLiFRy6Prd582Z8fX2dnaVYLl1pVPEqQQEBJCxdSuKyZSpdIiIiJcih4vXII48wbdo0jh07RnZ2trMzFYu2k7h+gZ98QrnXXwfDwFarFkb58u6OJCIi4lUcutS4fft2jh49ytq1azGZTJj/VHJKw871mvG6PoEff0zosGFYmzUDqxX8/d0dSURExOs4VLyefvppZ+e4bprxKr6gRYsIHT6cjJYtSZo3T6VLRETESQosXq1bt2blypWEh4cTExPjykzFouJVPEEffEDo//0fGW3akDR7NgQEuDuSiIiI1yqwrZw8eRK73e7KLOIG9goVSH/kEZLmzlXpEhERcTKvmSbSjFfRWA4fBiDjkUdIfv998PNzcyIRERHvV+g9Xvv27aO8AyvbGjVqVGKBik031zvGMAiZPJmQ6dNJWLOGrAYN9GcnIiLiIoUWr2eeeQbDMAr7EkwmEwcOHCjRUMWhGS8HGAblJkwg5L33SOvRg6w77nB3IhERkTKl0OK1fPlyIiIiXJXl+mjWpnCGQbnXXiNk9mxSY2O5MGGCzrcUERFxsQKLl8lkokqVKkSW+jP6cguXSkSh/DduzCldAwZwYexYFVURERE3KLB4XesSY+li6JDsa8h8+GES588n88EHVbpERETcpMBpopiYGPw9aSNNlYkr2WyUe+01LL/8AiYTmQ89pD8nERERNypwxmvixImuzHHddHP9n2RnE/b88wT+85/YK1cmtWZNdycSEREp8xw6MsgjaCbnf7KyCPvb3whct44LL79M6sCB7k4kIiIieFHx0oxXrsxMwp9+moBNm7gwZoxKl4iISCniNcVLM145TDYbposXOT9hAmn9+7s7joiIiFzGa4pXmZ/xSkvDZLdjhISQuHw5WCzuTiQiIiJ/4jXFqywz/HN2ogAAF8ZJREFUpaYSHhsLQOKKFSpdIiIipZTXTBOV1Rkv04ULRPTsid8PP5DWp482khURESnFvGfGqwwWDlNyMhG9e+O7bx/J779PRocO7o4kIiIihfCa4lUWd64Pe/55fP/7X5LmzMnZHFVERERKNa8pXmVxxuvC6NFYjh/H2rKlu6OIiIiIA7ymrZSVGS/z6dMEx8WBYWCrUUOlS0RExIN4z4xXGShe5t9/J7JbN8ynTpHRoQO26tXdHUlERESKwGuKl7fPeFlOnCCia1fMCQkkLlmi0iUiIuKBvKZ4efM9XpajR3NKV0oKicuWkdWwobsjiYiISDG4rHjZ7XbGjBnDzz//jJ+fH+PHjyc6Ojrv9XXr1rFgwQIsFgu33HILY8aMwVyEMuXNM14+v/6KKSuLhGXLyK5Xz91xREREpJhcNk20efNmrFYry5YtY+jQoUyaNCnvtYyMDN555x0WLlzI0qVLSUlJ4auvviraB3jhjJcpLQ2AzAce4My336p0iYiIeDiXtZWdO3fSokULABo0aMD+/fvzXvPz82Pp0qUEBgYCkJ2djb+/f5He39t2rvc5cIAKzZphWr0654mgIPcGEhERkevmskuNKSkphISE5D22WCxkZ2fj4+OD2WwmKioKgEWLFpGWlkazZs0KfT+LxUJkZCSQBUBkVJTXXG407d6NT7duEBCAqV693HF6Fx8fH68cF2hsnshbxyUipY/LildISAipqal5j+12Oz4+PvkeT548mSNHjhAXF3fNEmWz2UhISADKAZCYmOiU3K7mu3s3ET17YgsJIXHFCsKqV88dp3eJjIz0ynGBxuaJLh9X5cqV3ZxGRLyZy67PNWrUiK+//hqA3bt3c8stt+R7ffTo0WRmZjJjxoy8S45ljfnECSK6d8ceGkriP/+J7aab3B1JRERESpDLZrzatm3Ltm3b6NGjB4ZhMGHCBNauXUtaWhp169Zl5cqVNG7cmH79+gEQGxtL27ZtXRWvVLDfcAMpQ4aQ/uij2KtUcXccERERKWEuK15ms5mxY8fme65GjRp5vz548GCx3te4rlSlg98332CPiiL7tttIHTTI3XFERETESTx/KaCHNy//r74iIjaW8mPGuDuKiIiIOJnnFy8P5r9pE+F//SvZtWqRNHOmu+OIiIiIk6l4uUnAZ58R/uSTZNWpQ8Ly5RgREe6OJCIiIk7mJcXLw/bvMgwCP/6YrAYNSFy6FCMszN2JRERExAW845BsT+pd2dng40PS7NmY7HaMyzaVFREREe/mJTNeniFwyRIiO3fGdPEiBAWpdImIiJQxKl4uEvThh4QNG4Y9NBTDxzsmGkVERKRoVLxcIGjOHEJffpmMtm1J+uADKKM784uIiJR1Kl5OFrRoEaGvvkp6hw4kzZkD/v7ujiQiIiJuouLlZJn330/qk0+SPHMm+Pm5O46IiIi4kYqXMxgG/hs3gt2OrVo1LowdC7qvS0REpMxT8SpphkG5118n4oknCFi92t1pREREpBTRNExJMgzKv/oqwXPnktqvHxmdO7s7kYiIiJQimvEqKXY75V9+meC5c0l56ikuTJgAZv3xioiIyP9oxquE+Pz8M0Eff0zK3/7GxZdfBpMnbacvIiIirqDidb0MA0wmsm+7jbObN2OrUUOlS0RERK5K18KuR1YWYX/7G4ErVgBgq1lTpUtEREQKpOJVXFYr4YMGEbh6NeZz59ydRkRERDyAV1xqdPkcU0YG4QMHErB5M+fHjiXtySddnUBEREQ8kFcUL5fKzib8iScI+Ne/OD9pEmmxse5OJCIiIh5CxauofHzIuusuMh55hPSePd2dRkRERDyIipeDTCkpWE6eJLt2bVKGDHF3HBEREfFAurneAaYLF4jo2ZOIrl0xpaa6O46IiIh4KM14XYMpOZmIXr3w/e9/SZ45EyM42N2RRERExEN5R/Fy0rJGU0ICkT164HP4MElz55LZtq1zPkhERETKBO8oXk4SEheHT3w8iR9+iLVlS3fHEREREQ+n4lWIiyNHktG5M1kNGrg7ioiIiHgB3Vz/J+bffyds4EBMSUng76/SJSIiIiVGM16XsRw/TkTXrpiTkrAcP052eLi7I4mIiIgX0YxXLsvRo0Q89hjm8+dJXLaM7Hr13B1JREREvIxmvABLfDyR3bphysggYflysu+4w92RRERExAtpxgswAgKwValCwsqVKl0iIiLiNGV6xsvy22/YbrgB+w03kLBmDZictCGYiIiICGV4xstn716i2rWj3IQJOU+odImIiIiTlcni5fvjj0R264Y9OJi02Fh3xxEREZEywvOLl1G0L/f94QcievTAHh5O4qpV2KKjnZNLRERE5E/K1D1eprQ0wp98EnvFiiSsWIG9cmV3RxIREZEypEwVLyMoiOTZs8muXh17xYrujiMiIiJljOdfanSA/5YtBH70EQDWe+5R6RIRERG38Pri5b9xI+FPPEHQ4sWQleXuOCIiIlKGeXXxCli3jvCBA8mqW5fEpUvB19fdkURERKQM89riFbBqFWHPPENWw4YkLl2KERrq7kgiIiJSxnlt8bKcOoW1SRMSlyzBKFfO3XFEREREvK94mRISAEgdPDhnpis42M2JRERERHJ4VfEKmj+fis2b43PoUM4TPmVqtwwREREp5VxWvOx2O6NHj6Z79+707duXY8eO5Xv9yy+/pEuXLnTv3p3ly5cX7c1NEDx7NqGvvIL1nnvI1m70IiIiUgq5rHht3rwZq9XKsmXLGDp0KJMmTcp7LSsri4kTJ/LBBx+waNEili1bxtmzZx1/cwPKjxlDeseOJM2eDf7+ThiBiIiIyPVxWfHauXMnLVq0AKBBgwbs378/77X4+HiqVatGaGgofn5+3HnnnezYsaNI758eE0PyjBnaMkJERERKLZfdBJWSkkJISEjeY4vFQnZ2Nj4+PqSkpFDuspWHwcHBpKSkFPp+FouFyMhI6lX+lpDMC1g++ohIi8Vp+d3Fx8eHyMhId8cocd46LtDYPJG3jktESh+XFa+QkBBSU1PzHtvtdnxyb37/82upqan5itjV2Gw2EhIS+PS92kRGRpKQu5rR23jr2Lx1XKCxeaLLx1W5cmU3pxERb+ayS42NGjXi66+/BmD37t3ccsstea/VqFGDY8eOkZycjNVqZceOHTRs2NBV0URERERcwmQYhuGKD7Lb7YwZM4ZDhw5hGAYTJkzgp59+Ii0tje7du/Pll1/y3nvvYRgGXbp0oXfv3q6IJSIiIuIyLiteIiIiImWdV22gKiIiIlKaqXiJiIiIuIiKl4iIiIiLqHiJiIiIuIiKl4iIiIiLeEzxcuoh2252rbGtW7eOrl270qNHD0aPHo3dbndT0qK71tguGTVqFG+99ZaL0xXftca1d+9eevXqRc+ePXnuuefIzMx0U9Kiu9bY1qxZQ0xMDF26dGHJkiVuSnl99uzZQ9++fa943pP/HhERD2F4iM8//9wYPny4YRiGsWvXLmPQoEF5r1mtVqNNmzZGcnKykZmZaTz22GPGmTNn3BW1yAobW3p6utG6dWsjLS3NMAzDGDJkiLF582a35CyOwsZ2yccff2x069bNmDx5sqvjFVth47Lb7cajjz5qHD161DAMw1i+fLkRHx/vlpzFca3vWbNmzYykpCQjMzMz7393nmT27NlGx44dja5du+Z73tP/HhERz+AxM17OPmTbnQobm5+fH0uXLiUwMBCA7Oxs/P393ZKzOAobG8CuXbvYs2cP3bt3d0e8YitsXEeOHCEsLIwFCxbQp08fkpOTqV69uruiFtm1vme1a9fm4sWLWK1WDMPAZDK5I2axVatWjbi4uCue9/S/R0TEM3hM8SrokO1LrxX1kO3SpLCxmc1moqKiAFi0aBFpaWk0a9bMLTmLo7CxnTlzhunTpzN69Gh3xSu2wsaVlJTErl276NWrF/Pnz+e7775j+/bt7opaZIWNDaBWrVp06dKFDh060LJlS8qXL++OmMX20EMP5Z0TezlP/3tERDyDxxSvkj5kuzQpbGyXHr/xxhts27aNuLg4j5phKGxsGzduJCkpiYEDBzJ79mzWrVvHqlWr3BW1SAobV1hYGNHR0dSsWRNfX19atGhxxaxRaVbY2A4ePMi//vUvtmzZwpdffkliYiIbNmxwV9QS5el/j4iIZ/CY4uXNh2wXNjaA0aNHk5mZyYwZM/IuOXqKwsYWGxvLqlWrWLRoEQMHDqRjx4489thj7opaJIWNq2rVqqSmpubdlL5jxw5q1arllpzFUdjYypUrR0BAAP7+/lgsFiIiIrhw4YK7opYoT/97REQ8w5Xz7aVU27Zt2bZtGz169Mg7ZHvt2rV5h2yPGDGCAQMG5B2yXalSJXdHdlhhY6tbty4rV66kcePG9OvXD8gpLG3btnVzasdc6/vmqa41rtdff52hQ4diGAYNGzakZcuW7o7ssGuNrXv37vTq1QtfX1+qVatGTEyMuyNfF2/5e0REPIMOyRYRERFxEY+51CgiIiLi6VS8RERERFxExUtERETERVS8RERERFxExUtERETERVS8yoi+fftSu3btq/6zePFih95jxIgR9O/f3yn5Tpw4cUWuOnXq0Lx5c0aOHElycnKJfE5cXFy+rTh27drFzp078x7Xrl2bTz/9tEQ+62qffbUxNmvWjGHDhpGQkODwe2VnZ/Phhx86JaeIiDiPx+zjJdevY8eOjBgx4ornLz8ext1mzJhBvXr1gJwd0w8fPszw4cM5e/Ysc+fOve73f+KJJ+jdu3fe4z59+jBu3DjuvPNOALZu3erUI3BuuOEGli1blvc4MzOTPXv28Nprr5GcnOzwGNevX8/EiROdVoRFRMQ5VLzKkICAACpUqODuGIUKDQ3Nl7FSpUrExsYydepULly4cN2lKDg4mODg4LzHf97Gztl/PhaL5YrPuPHGGzl69CjTpk3j4sWLDh1To+33REQ8ky41Sp4TJ07w3HPP0aRJE26//XYeeOCBAmdgbDYbb7zxBi1atKBu3bo88sgj+c7ss9vtvP/++7Rq1YoGDRrQpUsX/v3vfxcrl8ViwWw24+vrC8ChQ4d46qmnuOuuu7j77rt56aWXSExMzPv6VatW0a5dO+rWrUurVq2YNm0adrsdyH+p8YEHHsBmszFy5Ej69u0L/O9S43fffUft2rU5fvx4viwdOnTg7bffBuCPP/7gueeeo1GjRtx7770MGTKE06dPF2uMfn5+mEwmLBYLAMnJyYwcOZLmzZtz++2307x5c9544w3sdjvff/89L730Ul7eS+db7tixgx49elCvXj1at27NlClTyMzMLFYeERFxDhUvyfPMM89gtVpZuHAh69evp1OnTkyePJkDBw5c8bVLlizhiy++IC4ujo0bN/Lwww8zdOjQvKIyZcoUVq1axdixY/n000+JiYnh2Wef5fvvv3c4j81mY9euXSxcuJD77ruPwMBATpw4Qc+ePQkNDeWjjz5ixowZHDx4kCeeeAKbzcbBgwcZPXo0Q4YMYdOmTbz88svMmzePNWvWXPH+K1euxGKx8PLLLxMXF5fvtSZNmnDDDTewfv36vOcOHDjAL7/8QufOnUlLS6Nv3774+/uzdOlS5s2bR1ZWFv369cNqtTo8RsMw2L17NwsXLqRNmzYEBQUBMHz4cOLj45k5cyYbN27kmWeeYf78+Xz55Zc0bNiQ0aNHAzmXRtu3b8+BAwcYMGAAbdu2Ze3atYwfP56vvvqKMWPGOJxFREScT5cay5DVq1fnKxIA7du35/XXXycjI4OYmBg6dOiQdz7ds88+y/vvv8/PP//Mbbfdlu/3HTt2jMDAQG644QYqVKjA4MGDqVevHmFhYaSmprJw4ULi4uJo0aIFANHR0Rw8eJDZs2fTpEmTAjMOGDAAsznn/w9kZmZiNptp3rw548ePB3IKX/ny5Zk4cWLeDNjbb79N+/bt+eabb8jKysJkMlGlSpW8f+bPn89f/vKXKz4rIiICyDn4OSwsLN9rJpOJRx99lHXr1vH0008DsGbNGho0aMDNN9/MihUrSE9PZ9KkSXmzVFOnTqVJkyZs2rSJjh07XnV8x48fz3fwstVqJSwsjHbt2jFkyJC851u0aEGTJk3yDtfu3bs3c+fO5eeff6ZNmzZ59+Vdumw5b9487r//fgYMGJD35/3aa6/Rq1cvhgwZQsWKFQv8MxcREddR8SpD2rRpw4svvpjvuUv3OwUEBNCnTx/Wr1/P3r17OXbsGAcOHMBut+ddprtcr169+OKLL7jvvvuoW7cuLVq0oFOnTpQrV469e/ditVp5/vnn80oUQFZWFlFRUYVmnDhxIrfffjsAvr6+REVF4efnl/f64cOHueOOO/JKF0CNGjUIDw/n0KFDxMbGUr9+fbp06UJ0dDTNmzenffv2VKlSpch/XjExMcycOZPDhw9To0YN1q9fz6BBgwD46aefSExMpHHjxvl+T3p6OvHx8QW+Z+XKlfNWIx47dozx48cTHR3NCy+8kO/es549e7JlyxZWrFjB0aNH+fnnnzl16tRVvxeQMxt37NixfKXu0n1g8fHxKl4iIqWEilcZEhISQnR09FVfS0tLo1evXthsNh566CGaNGlC/fr1adWq1VW/vnr16mzevJnt27ezbds2PvvsMz744ANmzZpFaGgokHM/1Z8/7/IidjUVK1YsMCOAv7//VZ+32+34+voSEBDA4sWL2bdvH19//TXffPMNS5YsYejQoTz11FOFfvafRUdH07BhQ9atW8e9995LYmIi7du3B3JKYc2aNZk+ffoVv6+wm+N9fHzyxhcdHc3cuXOJiYnhhRdeYM6cOZhMJgzDYODAgRw5coRHHnmETp06Ua9ePfr161fg+/r6+tK5c+erjrG0L6gQESlLdI+XAPDDDz9w4MABFi1axLPPPstDDz1EWloadrv9qivoPvroIzZt2sR9993HyJEj2bBhAzfeeCMbNmwgOjoaX19fTp8+TXR0dN4/a9euzbsRvLhq1qzJvn37yMrKynvul19+4fz589SoUYNt27bx3nvvcccdd/C3v/2NpUuX0qNHD/75z39e9f1MJlOhnxcTE8OmTZvYsGEDrVq1yiuVtWrV4sSJE4SFheWNLzIykokTJ3Lo0CGHx1OtWjWGDx/ON998k7fNxC+//MLWrVuJi4tjyJAhdOjQgfDwcM6ePZv3vfhz7po1axIfH5/vzzsxMZE33niD1NRUh/OIiIhzqXgJ8L/7ndauXcvJkyfZvn07L7zwAsBVbxZPSkpi3LhxfPXVV5w8eZItW7Zw4sQJ6tevT2BgIP3792fKlCmsX7+e48ePs3DhQt577z2qVq16XTn79OnDxYsXGTlyJIcPH2bHjh0MGzaMW2+9laZNm+Lr68t7773HwoULOX78OLt27eL777+nfv36V32/4OBgfvnllwI3L23fvj0nT55kzZo1dO7cOe/5Rx55hPDwcF544QX27dvHoUOHGDp0KHv27Mm7L8tRXbt25e677+att97i9OnTlC9fHh8fHzZs2MCJEyfYtWsXgwcPxmq15n0vLl2W3LdvH6mpqTz11FPs3buXiRMnEh8fzw8//MDw4cO5ePGiZrxEREoRXWoUAOrVq8dLL73EnDlzmDx5MlWqVOHxxx/n66+/Zt++ffTs2TPf1w8aNIiMjAxee+01zp07R+XKlfn73/9OTEwMAC+88AK+vr68+eabnDt3jqpVqzJ27Fgee+yx68oZFRXFBx98wOTJk+nSpQuBgYE88MAD/OMf/8DX15e7776bCRMmMHfuXN566y1CQkJo06ZN3vYLf/bUU08xY8YMvv32W1avXn3F6+XKlaN169Z899133HfffXnPBwQEMH/+fCZNmkS/fv0wmUw0aNCABQsWEBkZWaQxmUwmxo4dS6dOnRg3bhzTp09nwoQJxMXFsWDBAipVqkS7du2oVKkS+/btA3JWXd5999307NmToUOH8te//pVZs2bx7rvvsmTJEsqVK0erVq0KHLeIiLiHydBOjCIiIiIuoUuNIiIiIi6i4iUiIiLiIipeIiIiIi6i4iUiIiLiIipeIiIiIi6i4iUiIiLiIipeIiIiIi6i4iUiIiLiIipeIiIiIi7y/0zMQL9zxGOEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roc_curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The curves show that decision trees have the lowest performances, while random forest, logistic regression, and boosting have similar performances. We can note that the curves for the two decision trees have only a few points. For the tree with depth two, the reason is that it only has four leaves, so it only predicts four different values, and therefore has only four possible thresholds. For the tree with unlimited depth, the reason that is that all its leaves are pure on the training set (they either predict a probability of 1 or a probability of 0). Therefore this model only has two possible thresholds.\n",
    "\n",
    "ROC curves are relevant to get a sense of a classifier performance over the whole range of possible FPR. Their interest for fraud detection is however limited since an important goal of fraud detection is to keep the FPR very low. \n",
    "\n",
    "To get a sense of how low the FPR should be kept, let us recall that false positives are genuine transactions that are predicted as fraudulent. In an operational fraud system, these transactions will need to be manually handled by investigators. Due to the limited number of investigators, there is only a limited amount of transactions that can be checked. \n",
    "\n",
    "Let us consider more concretely how this constraint translates in terms of FPR. \n",
    "\n",
    "In this example, the dataset contains 58264 transactions (over 7 days), among which 57879 are genuine, and 385 fraudulent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(57879, 23)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_df[test_df.TX_FRAUD==0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(385, 23)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_df[test_df.TX_FRAUD==1].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming that 100 transactions can be checked every day, a total of 700 transactions could be checked after 7 days, that is, around 1% of the transactions. Therefore, any FPR higher than 0.01 will raise more alerts that can be handled by investigators.\n",
    "\n",
    "Real-world fraud detection systems typically handle hundreds of thousands to millions of on a daily basis. The proportion of transactions that can be manually checked is in fact closer to 0.1% than 1%. That is, any FPR higher than 0.001 is already too high. \n",
    "\n",
    "As a result, due to the imbalanced nature of the problem, 99.9% of what is represented on the ROC curve has little relevance from the perspective of an operational fraud detection system where fraudulent transactions must be checked by a limited team of investigators. \n",
    "\n",
    "We refer the reader to {cite}`saito2015precision` for an in-depth discussion of the inadequacy of the ROC curve for imbalanced problems, and the motivations for using the Precision-Recall curve instead.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Precision_Recall_Curve)=\n",
    "## Precision-Recall curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Precision-Recall curve (PR curve) is obtained by plotting the precision against the recall (or True Positive Rate - TPR) for all the different classification thresholds $t$. The main advantage of the PR curve is to put in evidence classifiers that can have both a high recall and a high precision (which indirectly translates to a high TPR and a low FPR).\n",
    "\n",
    "Let us reuse the same example as above, and compute the precision and recall for the eight unique thresholds.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Threshold</th>\n",
       "      <th>Precision</th>\n",
       "      <th>TPR</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.10</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.90</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.45</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.40</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.35</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.285714</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.222222</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.200000</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Threshold  Precision  TPR\n",
       "0       1.10   1.000000  0.0\n",
       "1       0.90   1.000000  0.5\n",
       "2       0.45   0.500000  0.5\n",
       "3       0.40   0.333333  0.5\n",
       "4       0.35   0.500000  1.0\n",
       "5       0.20   0.285714  1.0\n",
       "6       0.10   0.222222  1.0\n",
       "7       0.00   0.200000  1.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 fraudulent and 8 genuine transactions\n",
    "true_labels = [1,1,0,0,0,0,0,0,0,0]\n",
    "\n",
    "# Probability of fraud for each transaction\n",
    "fraud_probabilities = [0.9,0.35,0.45,0.4,0.2,0.2,0.2,0.1,0.1,0]\n",
    "\n",
    "unique_thresholds = [1.1]+list(set(fraud_probabilities))\n",
    "unique_thresholds.sort(reverse=True)\n",
    "\n",
    "performance_metrics=threshold_based_metrics(fraud_probabilities, true_labels, unique_thresholds)\n",
    "performance_metrics[['Threshold','Precision','TPR']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now plot the PR curve, and compute its AUC. We will use the Average Precision (AP), which summarizes such a plot as the weighted mean of precisions achieved at each threshold, with the increase in recall from the previous threshold used as the weight {cite}`boyd2013area,fan2011detection`.\n",
    "\n",
    "$$\n",
    "AP=\\sum_n(R_n-R_{n-1})*P_n\n",
    "$$\n",
    "\n",
    "where $P_n$ and $R_n$ are the precision and recall at the $n$-th threshold. \n",
    "\n",
    "An implementation of the average precision is provided below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_AP(precision, recall):\n",
    "    \n",
    "    AP = 0\n",
    "    \n",
    "    n_thresholds = len(precision)\n",
    "    \n",
    "    for i in range(1, n_thresholds):\n",
    "        \n",
    "        if recall[i]-recall[i-1]>=0:\n",
    "            \n",
    "            AP = AP+(recall[i]-recall[i-1])*precision[i]\n",
    "        \n",
    "    return AP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plotting is obtained by using the `step` function from `matplotlib`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "def get_template_pr_curve(ax, title,fs, baseline=0.5):\n",
    "    ax.set_title(title, fontsize=fs)\n",
    "    ax.set_xlim([-0.01, 1.01])\n",
    "    ax.set_ylim([-0.01, 1.01])\n",
    "    \n",
    "    ax.set_xlabel('Recall (True Positive Rate)', fontsize=fs)\n",
    "    ax.set_ylabel('Precision', fontsize=fs)\n",
    "    \n",
    "    ax.plot([0, 1], [baseline, baseline],'r--',label='AP Random = {0:0.3f}'.format(baseline))\n",
    "\n",
    "precision = performance_metrics.Precision.values\n",
    "recall = performance_metrics.TPR.values\n",
    "    \n",
    "pr_curve, ax = plt.subplots(figsize=(5,5))\n",
    "get_template_pr_curve(ax, \"Precision Recall (PR) Curve\",fs=15,baseline=sum(true_labels)/len(true_labels))\n",
    "AP2 = metrics.average_precision_score(true_labels, fraud_probabilities)\n",
    "AP = compute_AP(precision, recall)\n",
    "ax.step(recall, precision, 'b', color='blue', label = 'AP Classifier = {0:0.3f}'.format(AP))\n",
    "ax.legend(loc = 'lower right')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IyDB5SiOnpyrKg/Lat/LaL5C+lUWP9qsg97AWW4C6uLgQFhaW7d6z2NhYXFxclOd8mzRpwpEjR3J8JvtRGRkZyhMzjo6O2Z6eKS/Ka9/Ka79A+lYWPdqvgoxgVWwB2rZtW5PBLLI8ePAAW1tb5X2FChUKNIbkDz9YsXGjjrQ0h0JpZ2mj15fPvhV3v7p2TaZXr+S8ZxSiAEp8MBEbGxsSExOV94mJiSaB+iRarRZHR0dsbMzQaDT5GmW9LCqvfSvOfp04kVnX8OHWxVKfTqcr8p9CKSnltW9q+1XiAVqzZk2uXr1KQkIC1tbWHDlyhP79++e5XNYhvLc39OpVPg8r4Nk4ZCpqvr4OpKVBXFzhDACSl/L6nUH57VupP4R/XGRkJElJSfj5+TF27Fj69++P0WjE19f3mRkKSwhRthVrgFarVk25TenRMQRbtWqVbbQgIYQo7eRGeiGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVSSABVCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVSSABVCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVSSABVCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVQqtgA1GAwEBwfj5+dH7969uXr1qkn51q1b6dq1K76+vqxevbq4miWEEKrpiquiXbt2kZqayrp16zh+/DgzZ87k22+/Vcpnz57Ntm3bsLa2pn379rRv3x47O7viap4QQhRYsQXo0aNHadGiBQANGzbk9OnTJuW1a9fm/v376HQ6jEYjGo2muJomhBCqFFuAPnjwABsbG+W9VqslPT0dnS6zCW5ubvj6+mJlZUWbNm2oWLFiruvTarU4OjoCoNPplNflTXntW3H2S6/P3MaKq77y+p1B+e2b2n4VW4Da2NiQmJiovDcYDEp4nj9/nl9++YXdu3djbW3NqFGjiI6Oxtvb+4nry8jIIC4uDsj8j5H1urwpr30rzn6lpTkAEBd3p1jqK6/fGZTfvj3arypVquR7uWK7iNS4cWP2798PwPHjx3F3d1fKbG1tsbS0xMLCAq1Wi4ODA/fu3SuupgkhhCrFtgfapk0bDh48iL+/P0ajkRkzZhAZGUlSUhJ+fn74+fkREBCAXq/HxcWFrl27FlfThBBClWILUDMzM6ZMmWIyrWbNmsrrnj170rNnz+JqjhBCPDW5kV4IIVSSABVCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVSSABVCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVSSABVCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVSSABVCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFU0hVXRQaDgZCQEC5cuIC5uTnTpk3D1dVVKT958iQzZ87EaDTi5OTEnDlzsLCwKK7mCSFEgRXbHuiuXbtITU1l3bp1jBw5kpkzZyplRqORiRMnEhoaypo1a2jRogU3btworqYJIYQqxbYHevToUVq0aAFAw4YNOX36tFJ2+fJl7O3tWblyJTExMbRs2ZIaNWoUV9OEEEKVfAdoUlISERERHD9+nLS0NIxGo0n5smXLcl3+wYMH2NjYKO+1Wi3p6enodDri4+M5duwYEydOxNXVlYEDB1KvXj08PT2fuD6tVoujo2NmJ3Q65XV5U177Vpz90uszN/Piqq+8fmdQfvumtl/5DtBJkybx008/0aJFCypVqlTgimxsbEhMTFTeGwwGdLrM6u3t7XF1daVWrVoAtGjRgtOnT+caoBkZGcTFxQGZ/zGyXpc35bVvxdmvtDQHAOLi7hRLfeX1O4Py27dH+1WlSpV8L5fvAD148CCzZ8+mXbt2BW8d0LhxY/bu3YuPjw/Hjx/H3d1dKatevTqJiYlcvXoVV1dXjhw5Qvfu3VXVI4QQxSXfAZqRkUGdOnVUV9SmTRsOHjyIv78/RqORGTNmEBkZSVJSEn5+fkyfPp2RI0diNBpp1KgRb775puq6hBCiOOQ7QDt27MiqVauYMGECGo2mwBWZmZkxZcoUk2k1a9ZUXnt6erJhw4YCr1cIIUpKvgM0OTmZrVu38vPPP+Pi4oK5ublJeV4XkYQQorzJd4AaDAY6dOhQlG0RQogyJd8BGhoaWpTtEEKIMqdAN9KfPHmSZcuWcfHiRXQ6HbVq1SIwMBAPD4+iap8QQpRa+X6U89ChQwQEBHDz5k1atmyJp6cn165dIyAggN9//70o2yiEEKVSvvdA586dS8+ePRk/frzJ9NDQUL766itWr15d6I0TQojSLN97oOfPnycgICDbdD8/P86dO1eojRJCiLIg3wFauXJlbt68mW36zZs3sba2LtRGCSFEWZDvAPXx8WHSpEkcOnSIhw8fkpyczMGDBwkJCaFt27ZF2UYhhCiV8n0OdMiQIVy6dIl+/fqZPInk4+PDqFGjiqRxQghRmuU7QC0tLVm4cCGXLl3i4sWLWFhY4ObmRvXq1YuyfUIIUWrlGqD//PMPzz//vPIawNbWlsaNG5vMAyjzCSHEsyLXAH3zzTc5cOAAjo6OtGzZMsdBRIxGIxqNRq7ECyGeObkG6MqVK7GzswMgIiKiWBokhBBlRa4B+uqrr+b4OsudO3dwcHAo/FYJIUQZkO/bmO7evcv48eO5cOECBoOBgQMH0rx5c9q2bcvVq1eLso1CCFEq5TtAp0+fzrFjx9Dr9URHR3Po0CG+/PJL3N3dZaQmIcQzKd+3Me3bt48lS5ZQo0YNvvnmG9544w28vb1xd3fn3XffLco2CiFEqZTvPdDU1FScnJwA+PXXX2nevDkAGo0GM7N8r0YIIcqNfO+B1qlTh40bN+Lo6Eh8fDxvvvkmqamphIeHP9WPzQkhRFmV7wAdM2YMgwcPJj4+nv79+1O1alVCQkLYvXs3S5YsKco2CiFEqaQxGo3G/M5sMBi4f/++cm/otWvXqFSpEjY2NkXWwCdJTU0lLi4OAEdHR+V1eVNe+1ac/apatQoAnp4pxVKfXq8nLS2tWOoqbuW1b716aena9RYAVapUyfdyue6B/vHHHzRo0ACtVssff/yR4zy3bmVW+ujjnUIIUVacOaNn3Tro2rXgy+YaoAEBARw8eBBHR8ccB1POIo9yirJg48Y7xVJP5t518dRV3Mpj33x9HQC9qmVzDdDdu3crTxrt3r1bVQVCCFFe5Xr/kbOzszKAiLOzM1evXuXy5cs4Ozvj7OzMihUruHbtGs7OzsXSWCGEKE3yfQPnjz/+yIABA/jzzz+VaXfv3iUoKIjo6OgiaZwQQpRm+b6NafHixUyaNIkePXoo02bPnk3Tpk1ZsGAB3t7eRdJAIYQorfK9B3rjxg1ee+21bNM9PT3566+/CrVRQghRFuQ7QF1cXNi3b1+26QcPHizQfVNCCFFe5PsQvn///kyYMIGzZ89Sv359AE6fPs3WrVsJDg4usgYKIURple8A7dKlC+bm5kRERBAdHY1er6dGjRrMnTuXt99+uyjbKIQQpVK+AxQyf8LYx8enqNoihBBlSoHGobt79y6LFy9m3LhxxMXFsWPHDmJjY4uqbUIIUarlO0AvX76Mt7c3GzduJDIykqSkJHbu3En37t2f+Jy8EEKUZ/kO0NDQUNq2bctPP/2EXp/53Ojnn39Ou3bt+OKLL4qsgUIIUVrlO0BPnDhBr169TBc2M2PAgAGcPXu20BsmhBClXYHOgaakZB9PMS4uDnNz80JrkBBClBX5DtBWrVrx1VdfkZiYqEy7du0aM2bM4M033yyKtgkhRKmW7wAdN24cd+/epVmzZiQnJ9OjRw/eeecdzM3NGTNmTFG2UQghSqV83wealpbGunXr+PXXXzl37hx6vR43Nzc8PT2Lsn1CCFFq5TtAfX19CQsL4/XXX+f1118vyjYJIUSZkO9DeKPRKBeLhBDiEQXaAw0KCqJbt25Uq1YNS0tLk/KOHTsWeuOEEKI0y3eALliwAIBFixZlK9NoNBKgQohnTp4BmpSUxG+//UZ4eDiNGjWiQoUKqioyGAyEhIRw4cIFzM3NmTZtGq6urtnmmzhxInZ2dnz66aeq6hFCiOKSa4CeP3+eoKAgbt++jUaj4bnnniMsLAwPD48CV7Rr1y5SU1NZt24dx48fZ+bMmXz77bcm86xdu5aYmBheeeWVAq9fCCGKW64Xkb744guqV6/O2rVrWbduHS+++CKTJ09WVdHRo0dp0aIFAA0bNuT06dMm5ceOHePEiRP4+fmpWr8QQhS3XAP0+PHjBAcH07BhQzw8PJg2bRrnzp0jKSmpwBU9ePAAGxsb5b1WqyU9PR2Af//9l/nz58vI9kKIMiXXQ/jExEQqV66svK9evTparZaEhASsra0LVJGNjY3JY6AGgwGdLrP6HTt2EB8fz4ABA7h16xYPHz6kRo0adOvW7Ynr02q1ODo6ZnZCp1NelzfltW8l0a/iqq+8fmdQPvum1+vQaDSq+pVrgBoMBszMTHdSdTodGRkZBa6ocePG7N27Fx8fH44fP467u7tS1qdPH/r06QPApk2b+PPPP3MNT4CMjAzi4uKAzP8YWa/Lm/Lat+LtV+aPHhZXfeX1O4Py2be0NAf0er3Sr4L8SGaBftLjabRp04aDBw/i7++P0WhkxowZysDMct5TCFEW5RmgERERWFlZKe8zMjJYvXo1dnZ2JvMNHDgw1/WYmZkxZcoUk2k1a9bMNl9ee55CCFFa5BqgVatWJTIy0mRa5cqV+emnn0ymaTSaPANUCCHKm1wDdM+ePcXVDiGEKHMKNCK9EEKI/yMBKoQQKkmACiGEShKgQgihkgSoEEKoJAEqhBAqSYAKIYRKEqBCCKGSBKgQQqgkASqEECpJgAohhErFNpydECWlRYuUkm6CKKckQEW5t27dnZJugiin5BBeCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVSSABVCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVSSABVCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJQlQIYRQSQJUCCFUkgAVQgiVJECFEEIlCVAhhFBJAlQIIVSSABVCCJUkQIUQQiVdcVVkMBgICQnhwoULmJubM23aNFxdXZXybdu2sXLlSrRaLe7u7oSEhGBmJvkuhCi9ii2hdu3aRWpqKuvWrWPkyJHMnDlTKXv48CFfffUVERERrF27lgcPHrB3797iapoQQqhSbHugR48epUWLFgA0bNiQ06dPK2Xm5uasXbsWKysrANLT07GwsMj3unVt2uCQlmYy7WHHjiT17QtJSTj07p1tmeR33yXZzw9NXByVBgzIVp7Upw8PO3fG7MYN7IcNy1ae+OGHpLzzDtpLl7AbMyZb+YPhw0n18kJ3+jQVJ03KVn5/7FjSXnkF/f/8D7aP/DHJcm/yZNLr1UOzezcOU6dmK787axYZtWphsXMnFRYtylaeMG8eBmdnLLdswToiIlt5/OLFGB0dsVq3Dqv167OV31m1CqytsV6xAsvIyOzlGzcCUOHbb7HYtcukzGhpSfz33wNgM3cu5gcOmJQbKlWCzZsBsJ0xA/3Ro6blVaqQMH8+ABWDg9GdOWNSnlGjBnfnzAHAbtQotH/+aVKe/vLL3JsyBQD7IUMwu3nTpDytSRPuf/ZZZnlQEGbx8SblqW+8wYMRIwCo9N57aB4+NClPefttEmFzhVQAAB4dSURBVAcNAsDB15fHmfn7Q48eZX7bM9+/H5uvvzYp0+n1aKdNK9PbXkJ4OPB/257uzHxo2DBbPflRbAH64MEDbGxslPdarZb09HR0Oh1mZmZUrlwZgFWrVpGUlETz5s1zXZ9Wq8XR0REAjUaDXq83La9QAStHR7CyQvdYGYDWxgZrR0cwGnMst7W1pYKjIyQlPbHcxtERbt/OsbxixYoYHR3R2NujzaHczs4us9zOLsdye3t7jI6OaLXaJ5bj6IjG1jbH8kqVKoGjI2a2tpjlUO7g4JBZbmOTY7mjoyNYW2NWocKTywEza+vs5Xp97uXm5qDT4ejoiNbKCs1j5UYLC2V5raVltnLdo+UWFtnLLS3R51ZuZYX5/5brzM3h8W3H2hqLrHK9HjIyspVbPlr+uKxts4xve5qKFbOVazSaMr/tKdvO/25771fZAf0aKtMLQmM0Go0FXkqF0NBQGjRogI+PDwBeXl7s379fKTcYDMyZM4fLly8zd+5cZW/0SVJTU4mLiwMyP9Cs1+VNee1bee0XSN/Kokf7VaVKlXwvV2znQBs3bqwE5vHjx3F3dzcpDw4OJiUlhQULFuQZnkIIURoU2yF8mzZtOHjwIP7+/hiNRmbMmEFkZCRJSUnUq1ePDRs20LRpUwIDAwHo06cPbdq0Ka7mCSFEgRVbgJqZmTHlf0/sZ6lZs6by+vz588XVFCGEKBRyo6UQQqgkASqEECpJgAohhEoSoEIIoZIEqBBCqCQBKoQQKkmACiGEShKgQgihkgSoEEKoJAEqhBAqSYAKIYRKEqBCCKGSBKgQQqgkASqEECpJgAohhErFNh6oEKVJRkYG9+7dIz09vdDXHRcXh8FgKPT1lgblqW86nY6KFSui1WrVr6MQ2yNEmXHv3j0sLCywt7dHo9EU6rq1Wi0Zj/0QXXlRXvpmNBpJTk7m3r17mT+Cp5IcwotnUnp6OlZWVoUenqJs0Gg0WFlZPfURiASoeGZJeD7bCuP7l0N4IUrY6tWr2bBhA2vWrMHCwoLQ0FAuXryIra0tGo2GjIwMPvnkE/7zn/8oy0RHR7N8+XLlJ3gfPHhA/fr1+fjjj5+qLYMGDSI4OLhAP+37NLZt28bWrVvRarX07t2b119/3aT84sWLzJs3DzMzM8zNzRk3bhwODg45LpeSksL06dOJj4/H2tqacePGZf6GfRGSABWihO3atYtWrVqxZ88evL29Afjwww9p1qwZAIcPH2bZsmVMnTrVZLnWrVvz4YcfAmAwGBg2bBjnz5+nTp06xdsBleLi4ti4cSOLFi0iNTWVoUOH0rRpU8zNzZV55s+fz7Bhw3Bzc2Pr1q2sWbMGf3//HJfbsmUL//nPf5gyZQq7d+9m1apVDB06tEj7IAEqBODg65tt2sOOHUnq2xeSknDo3TtbefK775Ls54cmLo5KAwYo0zUaDXEbNuSr3mPHjlG1alU6derE9OnTlQB91L1797Cyssp1PUlJSTx48AAbGxsSExOZM2cODx484O7du3To0IHOnTszfPhwatWqxeXLl0lKSiIkJIQXXniB8PBwfv/9d5ycnLh79y4A9+/fZ/r06SQlJZGRkUH//v1p3LgxgYGBeHh48Oeff1K9enUqVarEyZMn0ev1zJo1C53u/yJl9uzZ3LhxQ3lfsWJFkz8C58+fp169epibm2Nubo6zszN//vmnyR+A4OBgHB0dgcw7J8zNzZ+43KlTp/D39wegWbNmrFq1Kl/fwdOQABWiBEVFRdG+fXtcXFzQ6/WcPXsWgEWLFrF69Wq0Wi2Ojo4MHDgw27K7d+/m7NmzxMXFYW1tTa9evahWrRoxMTG0atUKLy8vbt++zfDhw+ncuTMAdevWZejQoYSHh7N79248PT05ceIECxcuJDk5mV69egGwatUqmjZtSvfu3bl16xZDhw5l9erVJCUl0bp1az7++GN69+7NRx99RFBQEMOHD+fy5cu4ubkp7Rs9enSufU9MTMTGxkZ5b21tzYMHD0zmyQrP06dPs3nzZubNm8fvv/+e43KPri+ndRUFCVAhgDsbNz650No613Kjo6NJuVarhXzc6nP//n0OHz5MQkICmzZtIjExkc2bN2NmZmZyCP8kWYfwN2/eZPTo0VSrVg0ABwcHNmzYwP79+6lQoYLJleasgHNycuLOnTtcuXKF2rVrY2ZmRoUKFZTzrH/99Rdt2rRR5q1QoQIJCQkAuLu7A2BjY4Orq6vyOjU11aR9ee2BVqhQgaSkJOV9UlKSSTBm2bNnD9999x0zZ87E3t7+ics9Ov1J6ypsEqBClJCff/4ZHx8fBg0aBMDDhw/p2bMntWvXLtB6qlSpwvDhwwkJCWHFihWsW7eOl19+mc6dO3Ps2DF+++23Jy5bvXp1Nm3ahMFgICUlhatXrwLg4uLCyZMncXNz49atW9y/f5+KFSsWqF157YHWqVOH8PBwUlJSSEtL4+rVqyYXygB27txJZGQkX331lVL/k5arV68ev/32G3Xr1uXw4cN4eHgUqL1qSIAKUUKioqL47LPPlPeWlpZ4eXkRFRVF165dC7Supk2b0qRJE5YvX87rr7/Ol19+yc8//4ydnR1arTbb3mEWNzc3WrZsycCBA3F0dFSuWvfq1YtZs2axb98+UlJSGDlypMn5zcLg6OiIr68vw4YNw2g0EhQUhIWFBVeuXGHz5s0MGzaMsLAwnnvuOSZOnAhAw4YN6devX47Lde7cmdDQUIYMGYJer2fChAmF2t6caIxGo7HIaykCqampxMXFAZlfRNbr8qa89q2k+3Xr1i2cnJyKZN3l5WmdnJS3vmVtB49ujwW5hUtupBdCCJUkQIUQQiUJUCGEUEkCVAghVJIAFUIIlSRAhRBCJbkPVIgSpmY0JoCTJ0+ycuVK0tPTefjwId7e3nTp0oXo6Gj++usvZaARtS5evMivv/5KYGAgP/74I5GRkfj5+XHmzBlGjBjxVOvOSUJCAtOmTSMlJYXKlSszZswYLC0tlfLDhw+zevVq5f2pU6dYvnw5lSpVolevXsrn06JFC7p3786vv/7KypUr0Wq1+Pj40KFDh0JvswSoECVMzWhMf//9N/PmzWP27Nk4ODiQkpLCxx9/XKjD0Lm5uSmPfu7fv5/x48fj5ubGO++8U2h1PCoiIoLWrVvj7e3N999/T2RkJD169FDKmzVrpnwma9eupV69eri6unLkyBFat27N8OHDlXnT09OZP38+ixYtwtLSkiFDhuDp6ak8W19YJEDFM++HH6xYuzb30Y4KQqPR4OeXRI8eyXnOq3Y0pp07d9K2bVscHBwAsLCwYM6cOVhZWbFz505lvsWLF3PhwgWSkpJwdXVl7NixnDp1igULFqDT6bC1tWXChAnExcUxc+ZMdDodWq2WcePGcf36dbZu3Urjxo25cOECs2fPZvLkyYSEhPDtt99y/PhxwsPD0Wq1VK1alZEjR/Lzzz8THR2NwWCgX79+NGnSBMjcW166dKlJH959912aN2+uvD916hTvvfcekBmW4eHhJgGa5d9//2Xnzp0sXLgQgJiYGC5evMjw4cOxt7dn2LBhJCQk4OzsjK2tLQD169fn1KlTvPnmm3l+JwUhASpECVI7GlNcXBy1atUymfb44BmJiYnY2tryxRdfYDAY6Nu3L7du3eLAgQN4eXnh5+fHwYMHuX//PkeOHMHd3Z2PPvqIkydPcv/+fWU9HTt2ZNeuXXzyySfKKO5Go5HPP/+csLAwKlWqxNKlS9mxYwdarRZbW1umT59u0hYPDw++/vrrXD+L/I6m9MMPP9CjRw9l3FAXFxfc3d1p2rQpP//8M19//TXdu3fPc6SnwiABKp55PXok52tvMb/y+7jj04zG9Pzzz/Pvv/+aTLt06RKPPpltYWFBfHw8U6ZMwcrKiuTkZNLT0+nVqxerVq3ik08+oXLlyrz00kv4+PiwZs0aRo8eTYUKFQgKCsq17QkJCcTFxRESEgJkPlrdtGlTqlatSvXq1bPNn5890KzRlCwsLJ44mpLBYODQoUMm7WvcuDEWFhZA5vnP5cuX53ukp6clASpECXma0Zhat27NhAkTaNWqFfb29iQlJfHFF18QGBiozHP48GFu3brFpEmTSEhI4L///a9Sb7t27Rg8eLByrtHFxQUPDw/69u3L7t27WbNmDW3btn1i/XZ2djg5OTF9+nRsbGw4ePAgVlZW/PPPPzn+1lB+9kCzRlPy9vZ+4mhKly9fxsXFRQlMgDlz5uDl5cVbb73FH3/8gbu7O66urly/fl05/XHy5En8/Pzy/FwLSgJUiBLyNKMxValShYEDBzJx4kTMzMxITk6mffv2vPbaa0RHRwOZw75FREQwaNAgzM3NqVq1Krdv36ZOnTrMnDkTKysrdDodn376KQaDgenTp6PVajEzM+Ojjz4iMTHxifWbmZkxdOhQxo4di9FoxNrams8++4x//vlH9efRu3dvQkNDiYqKws7OThlNaeHChbRs2ZK6dety7dq1bBfKBgwYwKxZs/jxxx+xsrJi1KhR6HQ6PvroI0aNGoXRaMTb27tIBo+R0ZhKufLat5Lul4zGpE5565uMxiSEECVEAlQIIVSSABVCCJUkQMUzq4ye/heFpDC+/2ILUIPBQHBwMH5+fvTu3Vv58aose/bswdfXFz8/P9avX19czRLPKJ1OR3JysoToM8poNJKcnPzUv/NUbLcx7dq1i9TUVNatW8fx48eZOXMm3377LQBpaWmEhoayYcMGrKys6NmzJ2+99VaRXSUVomLFity7dy/XW3XUMjMzw2AwFPp6S4Py1DedTlfgXxrNto5Cakuejh49SosWLYDMX9Y7ffq0UhYbG4uLiwt2dnYANGnShCNHjuT4XLAQhUGr1VKpUqUiWXdJ36JVlMpz39QotgB98OCByaNUWq2W9PR0dDodDx48UB76h8xHuvJ6bjXrGWHI/EtS2KOslBbltW/ltV8gfSuL1Par2ALUxsbG5HDJYDAo5x8eL8saBCE3GRkZciN9GVZe+wXSt7Ko1N9I37hxY/bv3w/A8ePHcXd3V8pq1qzJ1atXSUhIIDU1lSNHjtCoUaPiapoQQqhSbI9yGgwGQkJCiImJwWg0MmPGDM6ePUtSUhJ+fn7s2bOHb775BqPRiK+vrzIuoBBClFZl9ll4IYQoaXIjvRBCqCQBKoQQKkmACiGEShKgQgihkgSoEEKoVGYCtDwPRpJX37Zt20aPHj3w9/cnODi4TD2LnFffskycOJHPP/+8mFunXl79OnnyJAEBAfTs2ZNhw4aRkpJSQi0tuLz6tnXrVrp27Yqvry+rV68uoVY+nRMnTtC7d+9s0wucI8Yy4qeffjKOGTPGaDQajceOHTMOHDhQKUtNTTW+/fbbxoSEBGNKSoqxW7duxn///bekmlpgufUtOTnZ2Lp1a2NSUpLRaDQaR4wYYdy1a1eJtFON3PqWZc2aNcZ3333XOGfOnOJunmq59ctgMBg7depkvHLlitFoNBrXr19vjI2NLZF2qpHXd9a8eXNjfHy8MSUlRfl/V5YsXrzY2KFDB2OPHj1MpqvJkTKzB5rfwUjMzc2VwUjKitz6Zm5uztq1a7GysgIgPT3d5BcJS7vc+gZw7NgxTpw4USS/mFiUcuvX5cuXsbe3Z+XKlfTq1YuEhARq1KhRUk0tsLy+s9q1a3P//n1SU1MxGo05/gpnaebi4kJYWFi26WpypMwE6JMGI8kqK+hgJKVJbn0zMzOjcuXKAKxatYqkpCST39Iu7XLr27///sv8+fMJDg4uqeapllu/4uPjOXbsGAEBASxfvpzffvuNQ4cOlVRTCyy3vgG4ubnh6+tL+/btefPNN596SLji1rZt2xzHAVWTI2UmQAt7MJLSJLe+Zb2fNWsWBw8eJCwsrEz9xc+tbzt27CA+Pp4BAwawePFitm3bxqZNm0qqqQWSW7/s7e1xdXWlVq1a6PV6WrRokW0vrjTLrW/nz5/nl19+Yffu3ezZs4c7d+4oP6Nc1qnJkTIToOV5MJLc+gYQHBxMSkoKCxYsUA7ly4rc+tanTx82bdrEqlWrGDBgAB06dKBbt24l1dQCya1f1atXJzExUbn4cuTIEdzc3EqknWrk1jdbW1ssLS2xsLBAq9Xi4ODAvXv3SqqphUpNjhTbcHZPq02bNhw8eBB/f39lMJLIyEhlMJKxY8fSv39/ZTCS559/vqSbnG+59a1evXps2LCBpk2bEhgYCGQGT5s2bUq41fmT1/dWVuXVr+nTpzNy5EiMRiONGjXizTffLOkm51teffPz8yMgIAC9Xo+Liwtdu3Yt6SY/lafJERlMRAghVCozh/BCCFHaSIAKIYRKEqBCCKGSBKgQQqgkASqEECpJgJYCrVq1onbt2ib/GjRogLe3NytWrCjWttSuXZstW7YAMHbsWPr27Zvr/AkJCbRr1474+Hh69+6drR+P/stp8IaiEhYWlq1+Dw8POnTowJo1awqtnlatWrFgwQIg8zHbR7+vTZs28dJLLxVaXTnVXVjbzc2bN4mKisr3/BcvXsTX19fkCaVnUZm5D7S8++CDD5T7PCEzmNauXUtoaCjPPfccPj4+Jdi6J5sxYwbdu3enUqVKhIWFkZaWBmQ+4z506FA2b96Mk5MTAHq9vljb5uzszLp165T3Dx8+ZMuWLYSEhGBnZ1con+mGDRuwtLQEYPv27YSGhip/dHx8fPDy8nrqOnJTWNvNZ599xvPPP0/79u3zNb+bmxt169ZlyZIlDBo0SFXbywPZAy0lrK2tcXJyUv65ubkxceJEXFxc2L59e0k3L0exsbHs3LmTnj17ApmPMGa1387ODgAHBwdlmr29fbG2T6vVmnym1atXZ8iQIbz44osF2tvKjYODA9bW1gA8fku1paWlMo5BUSms7UbN7eD9+vVjyZIl3L9/v8DLlhcSoKWcXq83eS7+5s2bDBs2jMaNG/P6668zYsQI/vnnH6XcaDSyYsUK3nnnHRo0aEDnzp3Zt2+fUv7TTz/h6+uLh4cHDRo0wN/fn5MnT6pq28qVK/Hy8qJChQr5XiYsLIzevXsrfZg7dy5hYWHZnqx6fFpe/S4InU6Hubm58n7Dhg106NABDw8P2rRpw3fffaeUJSUlMW7cOF5//XXq16/Pu+++azIwSNYh/OHDhxk9ejSQeRpk06ZNJofwY8aMyXYK4+TJk9SuXVt55HPXrl106tSJ+vXr065dO5YuXap67NfHt5vDhw/Tq1cvGjVqRL169ejcubPyuObYsWM5dOgQmzdvpnbt2kDm8+8LFy7krbfeomHDhvj6+ppsR5D56KOzs3OZG3+3MEmAllLJycmEh4cTGxtLx44dgcz/zL1798bCwoK1a9eydOlS0tLSCAwMJDU1FYAlS5Ywb948Bg8eTGRkJO3ateOjjz7i4sWLnDx5ko8//phu3bqxfft2Vq1aBWQOZqzGnj17VB2i/v7771SvXp3NmzfTvXv3POfPT7/zIzExkfDwcC5dukTbtm0BWL58OVOnTiUwMJCtW7fSv39/Zs+ezbJlywCYN28ely5dYunSpWzfvp26devy0UcfkZSUZLLuRo0aKaNKHThwINuhc5cuXThy5IhJ6EdGRtKoUSNcXV3Zt28fn376KX369CEqKopRo0YRERGhnF/Nr5y2m5s3b/LBBx/QpEkTtm7dyoYNG6hSpQpjxowhNTWV8ePH07RpU7y9vTlw4AAAX3zxBZs2bWLKlCls2bKFrl27MmTIEA4fPmxSX8uWLdmzZ0+B2lieyDnQUmLBggUsWbIEyNyLTElJoXbt2nz55Ze0bt0agKioKJKTk5k5cyZarRaAL7/8kmbNmrFz507at29PREQE/fr1o0uXLgAMGjSI9PR0kpKSMDc3Z9KkSfj7+wNQrVo1evTowYQJEwrc3r///ptbt26pGiRDo9EwdOhQ5dxhXvLqd4cOHXJc7tq1a8pgEEajkeTkZCpVqsQnn3xCu3btMBqNhIeHExgYSI8ePQB48cUXuXbtGkuWLKFfv35cvXqVChUqUK1aNWxtbRkzZgxt27ZV2pHF3NxcGQIu65zvo1577TVeeOEFtm/fTr9+/cjIyCA6OpohQ4YAsHDhQnr27Kn8QXFxcSExMZGJEycyePBgzMxy3tfJz3aTlpbG8OHDef/995WRvPr27UtgYCBxcXFUqVIFvV6PpaUlTk5OJCYmEhERQVhYmDIuqKurK+fPn2fx4sU0a9ZMqd/Nza3YL3SWJhKgpcR7771HQEAAGRkZ7N69mwULFtCtWzeTk/pnz57lzp07NG3a1GTZ5ORkYmNjiY+P59atW3h4eJiUDx06VHlta2vLokWLuHTpElevXuXcuXOqDhNv374NQKVKlQq8rJOTU77DE/Lu95NUqVJF+c+t0WiwtrY2OSd5584dbt++TePGjU2We+WVVwgPDycuLo7+/fszePBgPD09adSoES1atKBz584FHtRao9HQqVMntm3bRr9+/Th06BB3795V9lTPnTvHqVOnWLt2rbKMwWDg4cOH3Lhxg+rVq+e43vxsNy4uLnTp0oWVK1dy4cIF5XsHyMjIyLbO2NhYUlNTGT58uElwp6WlZTun6+DgQFpaGnfv3lXOez9LJEBLCTs7O1xdXQGoUaMGZmZmTJ8+HQcHB2UPS6/XU6tWLebPn59teVtb2zyvcv/222988MEHtG7dmsaNG+Pr68uVK1eYNGlSgdubtSejJnzzE56P3h6TV7+fRKfTKZ9pTp4UglmhotPpaNq0Kfv27ePAgQMcOHCA77//nmXLlvHdd99Rq1atPPvxqK5du7Jw4UKuXLnCtm3baNWqlTIYsV6vJygoSDnsflRuIwLlZ7u5ePEiAQEBNGjQAE9PT3x8fEhPT2fgwIE5rjPr/HBYWFi2z+/xPeGsz+rxPfJnhZwDLaXef/99mjRpwuTJk7l16xaQebh0/fp1ZcBeV1dXHB0dCQ0NJSYmBltbW5ycnDh16pTJunr37k14eDirV6+mefPmfPXVV/Tp04fXXnuNGzduAAW/Cvvcc88BmXtxT0uv15sMZAuY/JBZXv1Wy8bGhhdeeIGjR4+aTD969KhyJ8H8+fP5448/aNOmDZMnT2bnzp0YDAb27t2bbX15DXT94osv0qhRI6Kioti1a5fJMHC1atXiypUrSv9cXV2JiYlh7ty5BepTTtvNpk2bqFKlCuHh4fTv358WLVoo52KzvvdH2+7q6oper+eff/4xaU9kZGS2Aa/j4+OxsrIyGcH+WSIBWkppNBqmTp3Kw4cPmTZtGgAdO3akUqVKfPzxx5w6dYqYmBhGjhzJiRMnlHORQUFBrFixgqioKP766y8WLFjAiRMnaNmyJQ4ODly4cIHjx49z7do1Vq1axcqVKwEKdDEGMveKnn/+eeVQ8Gk0bNiQuLg4VqxYwfXr11m9erVyhTi//VZr0KBBRERE8MMPP3D16lXWr1/Pd999R9++fdFoNNy4cYPJkydz+PBhbty4wdatW7l//z4NGjTItq6suxFOnTqV7Q9Cli5durB06VLMzc154403TNoRFRXF4sWLuXLlCr/88gvBwcFYWlqa3DGQl5y2GwcHB27cuMHBgwe5ceMGW7ZsUYI563uvUKEC169f58aNG1hZWdG3b1+++OILtm/fzrVr14iIiOCbb77JdirhzJkz2U4ZPUskQEuxmjVr8uGHH7Jjxw52796NpaUly5cvx9LSksDAQHr27El6ejorV67E0dERyBxsOSgoiDlz5tChQwd2797NwoULcXNzY9iwYdStW5f+/fvj6+vLzp07mTlzJkC2vdb8eOutt7JdlVXjtddeY+jQoSxZsoT27dtz6NAhhg0bppTnp99q+fv7M2LECBYtWkT79u1Zvnw5Y8eOJSgoCIAJEybw2muvMXLkSNq2bcuKFSsIDQ3l1VdfzbauZs2a8eqrr9KzZ88n3tqTdfjcoUMHk9uMvLy8mD17NpGRkXTo0IHg4GC6dOnClClTCtynx7ebrAG4R4wYQadOnfj++++ZPHky1tbWyvf+3nvvcfnyZXx8fLh16xYff/wxPXv2ZPbs2Xh7e7NmzRqmTJmS7RcDfv/9d+Vi1bNIBlQWql28eJHu3buzb9++Yr9JXpS8c+fO0atXL/bu3VvmfliusMgeqFDNzc2Nt99+2+TKsXh2ZN0y96yGJ0iAiqc0fvx4Nm/eXCgXk0TZERMTw/nz5xkwYEBJN6VEySG8EEKoJHugQgihkgSoEEKoJAEqhBAqSYAKIYRKEqBCCKGSBKgQQqj0/wHBkkDDYUDQLwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr_curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PR curves behave differently from ROC curves. We detail these differences in the following. \n",
    "\n",
    "First, they are not monotonic: The precision may decrease or increase, as the recall increases. This is illustrated above, where for a recall of $0.5$, the precision first goes down to $0.33$ (threshold $0.4$), before going up to $0.5$ (threshold $0.35$). \n",
    "\n",
    "Second, their AUC does not carry a statistical interpretation as ROC AUC. However, it can be shown that there exists a one-to-one correspondence between PR and ROC curves, and that a curve that dominates in the PR space necessarily dominates in the ROC space {cite}`davis2006relationship`. \n",
    "\n",
    "Third, the performance of a random classifier depends on the class imbalance. It is $0.5$ in the balanced case, and $P/(P+N)$ in the general case, where $P$ is the number of positive examples, and $N$ the number of negative examples. In particular, a classifier that classifies all examples as positive (recall of 1) has a precision of $P/(P+N)$. In the example above, this gives a precision of $2/(2+8)=0.2$, highlighted with the dotted red line. This property makes the AP more interesting than the AUC ROC in a fraud detection problem, since it better reflects the challenge related to the class imbalance problem (the AP of a random classifier decreases as the class imbalance ratio increases).  \n",
    "\n",
    "```{warning}\n",
    "Linear interpolation (as is used for ROC curves) should not be used for plotting PR curves, nor for assessing their AUC. The use of the step-wise function for plotting, and AP as a measure of AUC are well established. We refer the reader to {cite}`saito2015precision,flach2015precision,davis2006relationship` for detailed discussions on the topic, and the use of alternative ways to plot the PR curve or assess its AUC.  \n",
    "```\n",
    "\n",
    "Let us finally reuse the experimental setting of the previous section, and plot the PR curves and corresponding AP for each of the five prediction models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": [
     "hide-cell"
    ]
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "pr_curve, ax = plt.subplots(1, 1, figsize=(6,6))\n",
    "cmap = plt.get_cmap('jet')\n",
    "colors={'Logistic regression':cmap(0), 'Decision tree with depth of two':cmap(200), \n",
    "        'Decision tree - unlimited depth':cmap(250),\n",
    "        'Random forest':cmap(70), 'XGBoost':cmap(40)}\n",
    "\n",
    "get_template_pr_curve(ax, \"Precision Recall (PR) Curve\\nTest data\",fs=15,baseline=sum(test_df[output_feature])/len(test_df[output_feature]))\n",
    "    \n",
    "for classifier_name in classifiers_dictionary:\n",
    "    \n",
    "    model_and_predictions=fitted_models_and_predictions_dictionary[classifier_name]\n",
    "\n",
    "    precision, recall, threshold = metrics.precision_recall_curve(test_df[output_feature], model_and_predictions['predictions_test'])\n",
    "    precision=precision[::-1]\n",
    "    recall=recall[::-1]\n",
    "    \n",
    "    AP = metrics.average_precision_score(test_df[output_feature], model_and_predictions['predictions_test'])\n",
    "    \n",
    "    ax.step(recall, precision, 'b', color=colors[classifier_name], label = 'AP {0}= {1:0.3f}'.format(classifier_name,AP))\n",
    "    ax.legend(loc = 'upper left',bbox_to_anchor=(1.05, 1))\n",
    "    \n",
    "    \n",
    "plt.subplots_adjust(wspace=0.5, hspace=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr_curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let us compare these PR curves with the ROC curves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roc_curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At first sight, PR and ROC curves give a very different picture of the relative performances of the different classifiers. In order to better relate the two types of curve, it is useful to mentally 'transpose' the PR curve in such a way that the x-axis represents the precision, and the y-axis represents the True Positive Rate. Once transposed, both curves represent the TPR on their y-axis, and one can note that the PR curve is actually a zoomed version of the ROC curves for very low values of the False Positive Rate.\n",
    "\n",
    "As pointed out above at the end of the section on ROC curves, the TPR for low FPR values is actually what matters in a fraud detection problem: The number of cards that can be manually checked by fraud investigators is in practice very limited. This also gives a different ordering of performances for the classifiers. For example, with ROC curves, decision trees with unlimited depth have a better AUC than a decision tree of depth two (0.788 versus 0.763, respectively). The performances are reversed when computed in terms of Average Precision (0.309 versus 0.496). \n",
    "\n",
    "While PR curves are useful to highlight the performances of fraud detection systems for low FPR values, they however remain difficult to interpret from an operational point of view. The next section addresses this issue, by discussing [Precision top-$k$ metrics](Precision_Top_K_Metrics).\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
